TY  - JOUR
AU  - Gligorić, Goran
AU  - Radosavljević, Ana
AU  - Petrović, Jovana S.
AU  - Maluckov, Aleksandra
AU  - Hadžievski, Ljupčo
AU  - Malomed, Boris A.
PY  - 2017
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1848
AB  - We address the stability and dynamics of eigenmodes in linearly shaped strings (dimers, trimers, tetramers, and pentamers) built of droplets in a binary Bose-Einstein condensate (BEC). The binary BEC is composed of atoms in two pseudo-spin states with attractive interactions, dressed by properly arranged laser fields, which induce the (pseudo-) spin-orbit (SO) coupling. We demonstrate that the SO-coupling terms help to create eigenmodes of particular types in the strings. Dimer, trimer, and pentamer eigenmodes of the linear system, which correspond to the zero eigenvalue (EV, alias chemical potential) extend into the nonlinear ones, keeping an exact analytical form, while tetramers do not admit such a continuation, because the respective spectrum does not contain a zero EV. Stability areas of these modes shrink with the increasing nonlinearity. Besides these modes, other types of nonlinear states, which are produced by the continuation of their linear counterparts corresponding to some nonzero EVs, are found in a numerical form (including ones for the tetramer system). They are stable in nearly entire existence regions in trimer and pentamer systems, but only in a very small area for the tetramers. Similar results are also obtained, but not displayed in detail, for hexa-and septamers.
T2  - Chaos
T1  - Models of spin-orbit-coupled oligomers
VL  - 27
IS  - 11
DO  - 10.1063/1.5000345
ER  - 

@article{
author = "Gligorić, Goran and Radosavljević, Ana and Petrović, Jovana S. and Maluckov, Aleksandra and Hadžievski, Ljupčo and Malomed, Boris A.",
year = "2017",
abstract = "We address the stability and dynamics of eigenmodes in linearly shaped strings (dimers, trimers, tetramers, and pentamers) built of droplets in a binary Bose-Einstein condensate (BEC). The binary BEC is composed of atoms in two pseudo-spin states with attractive interactions, dressed by properly arranged laser fields, which induce the (pseudo-) spin-orbit (SO) coupling. We demonstrate that the SO-coupling terms help to create eigenmodes of particular types in the strings. Dimer, trimer, and pentamer eigenmodes of the linear system, which correspond to the zero eigenvalue (EV, alias chemical potential) extend into the nonlinear ones, keeping an exact analytical form, while tetramers do not admit such a continuation, because the respective spectrum does not contain a zero EV. Stability areas of these modes shrink with the increasing nonlinearity. Besides these modes, other types of nonlinear states, which are produced by the continuation of their linear counterparts corresponding to some nonzero EVs, are found in a numerical form (including ones for the tetramer system). They are stable in nearly entire existence regions in trimer and pentamer systems, but only in a very small area for the tetramers. Similar results are also obtained, but not displayed in detail, for hexa-and septamers.",
journal = "Chaos",
title = "Models of spin-orbit-coupled oligomers",
volume = "27",
number = "11",
doi = "10.1063/1.5000345"
}

Gligorić, G., Radosavljević, A., Petrović, J. S., Maluckov, A., Hadžievski, L.,& Malomed, B. A.. (2017). Models of spin-orbit-coupled oligomers. in Chaos, 27(11).
https://doi.org/10.1063/1.5000345

Gligorić G, Radosavljević A, Petrović JS, Maluckov A, Hadžievski L, Malomed BA. Models of spin-orbit-coupled oligomers. in Chaos. 2017;27(11).
doi:10.1063/1.5000345 .

Gligorić, Goran, Radosavljević, Ana, Petrović, Jovana S., Maluckov, Aleksandra, Hadžievski, Ljupčo, Malomed, Boris A., "Models of spin-orbit-coupled oligomers" in Chaos, 27, no. 11 (2017),
https://doi.org/10.1063/1.5000345 . .

TY  - JOUR
AU  - Gligorić, Goran
AU  - Maluckov, Aleksandra
AU  - Hadžievski, Ljupčo
AU  - Flach, Sergej
AU  - Malomed, Boris A.
PY  - 2016
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8840
AB  - We report the coexistence and properties of stable compact localized states (CLSs) and discrete solitons (DSs) for nonlinear spinor waves on a flat-band network with spin-orbit coupling (SOC). The system can be implemented by means of a binary Bose-Einstein condensate loaded in the corresponding optical lattice. In the linear limit, the SOC opens a minigap between flat and dispersive bands in the systems band-gap structure, and preserves the existence of CLSs at the flat-band frequency, simultaneously lowering their symmetry. Adding on-site cubic nonlinearity, the CLSs persist and remain available in an exact analytical form, with frequencies that are smoothly tuned into the minigap. Inside of the minigap, the CLS and DS families are stable in narrow areas adjacent to the FB. Deep inside the semi-infinite gap, both the CLSs and DSs are stable too.
T2  - Physical Review B: Condensed Matter and Materials Physics
T1  - Nonlinear localized flat-band modes with spin-orbit coupling
VL  - 94
IS  - 14
SP  - 144302
DO  - 10.1103/PhysRevB.94.144302
ER  - 

@article{
author = "Gligorić, Goran and Maluckov, Aleksandra and Hadžievski, Ljupčo and Flach, Sergej and Malomed, Boris A.",
year = "2016",
abstract = "We report the coexistence and properties of stable compact localized states (CLSs) and discrete solitons (DSs) for nonlinear spinor waves on a flat-band network with spin-orbit coupling (SOC). The system can be implemented by means of a binary Bose-Einstein condensate loaded in the corresponding optical lattice. In the linear limit, the SOC opens a minigap between flat and dispersive bands in the systems band-gap structure, and preserves the existence of CLSs at the flat-band frequency, simultaneously lowering their symmetry. Adding on-site cubic nonlinearity, the CLSs persist and remain available in an exact analytical form, with frequencies that are smoothly tuned into the minigap. Inside of the minigap, the CLS and DS families are stable in narrow areas adjacent to the FB. Deep inside the semi-infinite gap, both the CLSs and DSs are stable too.",
journal = "Physical Review B: Condensed Matter and Materials Physics",
title = "Nonlinear localized flat-band modes with spin-orbit coupling",
volume = "94",
number = "14",
pages = "144302",
doi = "10.1103/PhysRevB.94.144302"
}

Gligorić, G., Maluckov, A., Hadžievski, L., Flach, S.,& Malomed, B. A.. (2016). Nonlinear localized flat-band modes with spin-orbit coupling. in Physical Review B: Condensed Matter and Materials Physics, 94(14), 144302.
https://doi.org/10.1103/PhysRevB.94.144302

Gligorić G, Maluckov A, Hadžievski L, Flach S, Malomed BA. Nonlinear localized flat-band modes with spin-orbit coupling. in Physical Review B: Condensed Matter and Materials Physics. 2016;94(14):144302.
doi:10.1103/PhysRevB.94.144302 .

Gligorić, Goran, Maluckov, Aleksandra, Hadžievski, Ljupčo, Flach, Sergej, Malomed, Boris A., "Nonlinear localized flat-band modes with spin-orbit coupling" in Physical Review B: Condensed Matter and Materials Physics, 94, no. 14 (2016):144302,
https://doi.org/10.1103/PhysRevB.94.144302 . .

TY  - JOUR
AU  - Gligorić, Goran
AU  - Maluckov, Aleksandra
AU  - Hadžievski, Ljupčo
AU  - Flach, Sergej
AU  - Malomed, Boris A.
PY  - 2016
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1287
AB  - We report the coexistence and properties of stable compact localized states (CLSs) and discrete solitons (DSs) for nonlinear spinor waves on a flat-band network with spin-orbit coupling (SOC). The system can be implemented by means of a binary Bose-Einstein condensate loaded in the corresponding optical lattice. In the linear limit, the SOC opens a minigap between flat and dispersive bands in the systems band-gap structure, and preserves the existence of CLSs at the flat-band frequency, simultaneously lowering their symmetry. Adding on-site cubic nonlinearity, the CLSs persist and remain available in an exact analytical form, with frequencies that are smoothly tuned into the minigap. Inside of the minigap, the CLS and DS families are stable in narrow areas adjacent to the FB. Deep inside the semi-infinite gap, both the CLSs and DSs are stable too.
T2  - Physical Review B: Condensed Matter and Materials Physics
T1  - Nonlinear localized flat-band modes with spin-orbit coupling
VL  - 94
IS  - 14
SP  - 144302
DO  - 10.1103/PhysRevB.94.144302
ER  - 

@article{
author = "Gligorić, Goran and Maluckov, Aleksandra and Hadžievski, Ljupčo and Flach, Sergej and Malomed, Boris A.",
year = "2016",
abstract = "We report the coexistence and properties of stable compact localized states (CLSs) and discrete solitons (DSs) for nonlinear spinor waves on a flat-band network with spin-orbit coupling (SOC). The system can be implemented by means of a binary Bose-Einstein condensate loaded in the corresponding optical lattice. In the linear limit, the SOC opens a minigap between flat and dispersive bands in the systems band-gap structure, and preserves the existence of CLSs at the flat-band frequency, simultaneously lowering their symmetry. Adding on-site cubic nonlinearity, the CLSs persist and remain available in an exact analytical form, with frequencies that are smoothly tuned into the minigap. Inside of the minigap, the CLS and DS families are stable in narrow areas adjacent to the FB. Deep inside the semi-infinite gap, both the CLSs and DSs are stable too.",
journal = "Physical Review B: Condensed Matter and Materials Physics",
title = "Nonlinear localized flat-band modes with spin-orbit coupling",
volume = "94",
number = "14",
pages = "144302",
doi = "10.1103/PhysRevB.94.144302"
}

Gligorić, G., Maluckov, A., Hadžievski, L., Flach, S.,& Malomed, B. A.. (2016). Nonlinear localized flat-band modes with spin-orbit coupling. in Physical Review B: Condensed Matter and Materials Physics, 94(14), 144302.
https://doi.org/10.1103/PhysRevB.94.144302

Gligorić G, Maluckov A, Hadžievski L, Flach S, Malomed BA. Nonlinear localized flat-band modes with spin-orbit coupling. in Physical Review B: Condensed Matter and Materials Physics. 2016;94(14):144302.
doi:10.1103/PhysRevB.94.144302 .

Gligorić, Goran, Maluckov, Aleksandra, Hadžievski, Ljupčo, Flach, Sergej, Malomed, Boris A., "Nonlinear localized flat-band modes with spin-orbit coupling" in Physical Review B: Condensed Matter and Materials Physics, 94, no. 14 (2016):144302,
https://doi.org/10.1103/PhysRevB.94.144302 . .

TY  - CONF
AU  - Beličev, Petra
AU  - Gligorić, Goran
AU  - Maluckov, Aleksandra
AU  - Petrović, Jovana S.
AU  - Hadžievski, Ljupčo
AU  - Malomed, Boris A.
PY  - 2015
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/10953
AB  - The use of ultracold quantum gases, in particular bosonic and fermionic condensates, for simulating fundamental effects originating in condensed-matter physics has drawn much interest [1]. One of these effects is the spin-orbit coupling (SOC). This effect plays a major role in many phenomena and applications, including spin and anomalous Hall effects [2], topological insulators [3], spintronics [4], etc. In contrast to the complex picture found in solids, the experimental and theoretical description of SOC effects in Bose-Einstein condensate (BEC) is much simpler [5]. This has motivated our study of the impact of SOC on the immiscibility-miscibility transition in the localized complexes in BEC, which can emulate the phase transition between insulating and conducting states in semiconductor. For this purpose, we introduce a discrete model for binary SO-coupled BEC trapped in a deep one-dimensional optical lattice [6]. We consider two different types of coupling, with spatial derivatives acting inside each species, and between the species. Stable localized composite states of miscible and immiscible types are found to exist for both types of coupling. We also study how the transition between miscible and immiscible type of localized complexes depends on the SOC strength. Particularly interesting are the applications of our model to the SOC binary condensates built of infinitely heavy atoms and the binary BEC with effective atomic masses which have opposite signs.
PB  - Belgrade : Vinča Institute of Nuclear Sciences
C3  - PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade
T1  - Composite localized modes in discretized spin-orbit-coupled Bose- Einstein condensates
SP  - 48
EP  - 49
UR  - https://hdl.handle.net/21.15107/rcub_vinar_10953
ER  - 

@conference{
author = "Beličev, Petra and Gligorić, Goran and Maluckov, Aleksandra and Petrović, Jovana S. and Hadžievski, Ljupčo and Malomed, Boris A.",
year = "2015",
abstract = "The use of ultracold quantum gases, in particular bosonic and fermionic condensates, for simulating fundamental effects originating in condensed-matter physics has drawn much interest [1]. One of these effects is the spin-orbit coupling (SOC). This effect plays a major role in many phenomena and applications, including spin and anomalous Hall effects [2], topological insulators [3], spintronics [4], etc. In contrast to the complex picture found in solids, the experimental and theoretical description of SOC effects in Bose-Einstein condensate (BEC) is much simpler [5]. This has motivated our study of the impact of SOC on the immiscibility-miscibility transition in the localized complexes in BEC, which can emulate the phase transition between insulating and conducting states in semiconductor. For this purpose, we introduce a discrete model for binary SO-coupled BEC trapped in a deep one-dimensional optical lattice [6]. We consider two different types of coupling, with spatial derivatives acting inside each species, and between the species. Stable localized composite states of miscible and immiscible types are found to exist for both types of coupling. We also study how the transition between miscible and immiscible type of localized complexes depends on the SOC strength. Particularly interesting are the applications of our model to the SOC binary condensates built of infinitely heavy atoms and the binary BEC with effective atomic masses which have opposite signs.",
publisher = "Belgrade : Vinča Institute of Nuclear Sciences",
journal = "PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade",
title = "Composite localized modes in discretized spin-orbit-coupled Bose- Einstein condensates",
pages = "48-49",
url = "https://hdl.handle.net/21.15107/rcub_vinar_10953"
}

Beličev, P., Gligorić, G., Maluckov, A., Petrović, J. S., Hadžievski, L.,& Malomed, B. A.. (2015). Composite localized modes in discretized spin-orbit-coupled Bose- Einstein condensates. in PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade
Belgrade : Vinča Institute of Nuclear Sciences., 48-49.
https://hdl.handle.net/21.15107/rcub_vinar_10953

Beličev P, Gligorić G, Maluckov A, Petrović JS, Hadžievski L, Malomed BA. Composite localized modes in discretized spin-orbit-coupled Bose- Einstein condensates. in PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade. 2015;:48-49.
https://hdl.handle.net/21.15107/rcub_vinar_10953 .

Beličev, Petra, Gligorić, Goran, Maluckov, Aleksandra, Petrović, Jovana S., Hadžievski, Ljupčo, Malomed, Boris A., "Composite localized modes in discretized spin-orbit-coupled Bose- Einstein condensates" in PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade (2015):48-49,
https://hdl.handle.net/21.15107/rcub_vinar_10953 .

TY  - JOUR
AU  - Beličev, Petra
AU  - Gligorić, Goran
AU  - Petrović, Jovana S.
AU  - Maluckov, Aleksandra
AU  - Hadžievski, Ljupčo
AU  - Malomed, Boris A.
PY  - 2015
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/443
AB  - We introduce a discrete model for binary spin-orbit-coupled Bose-Einstein condensates trapped in a deep one-dimensional optical lattice. Two different types of the couplings are considered, with spatial derivatives acting inside each species, or between the species. The discrete system with inter-site couplings dominated by the spin-orbit coupling (SOC), while the usual hopping is negligible, emulates condensates composed of extremely heavy atoms, as well as those with opposite signs of the effective atomic masses in the two components. Stable localized composite states of miscible and immiscible types are constructed. The effect of the SOC on the immiscibility-miscibility transition in the localized complexes, which emulates the phase transition between insulating and conducting states in semiconductors, is studied.
T2  - Journal of Physics. B: Atomic Molecular and Optical Physics
T1  - Composite localized modes in discretized spin-orbit-coupled Bose-Einstein condensates
VL  - 48
IS  - 6
DO  - 10.1088/0953-4075/48/6/065301
ER  - 

@article{
author = "Beličev, Petra and Gligorić, Goran and Petrović, Jovana S. and Maluckov, Aleksandra and Hadžievski, Ljupčo and Malomed, Boris A.",
year = "2015",
abstract = "We introduce a discrete model for binary spin-orbit-coupled Bose-Einstein condensates trapped in a deep one-dimensional optical lattice. Two different types of the couplings are considered, with spatial derivatives acting inside each species, or between the species. The discrete system with inter-site couplings dominated by the spin-orbit coupling (SOC), while the usual hopping is negligible, emulates condensates composed of extremely heavy atoms, as well as those with opposite signs of the effective atomic masses in the two components. Stable localized composite states of miscible and immiscible types are constructed. The effect of the SOC on the immiscibility-miscibility transition in the localized complexes, which emulates the phase transition between insulating and conducting states in semiconductors, is studied.",
journal = "Journal of Physics. B: Atomic Molecular and Optical Physics",
title = "Composite localized modes in discretized spin-orbit-coupled Bose-Einstein condensates",
volume = "48",
number = "6",
doi = "10.1088/0953-4075/48/6/065301"
}

Beličev, P., Gligorić, G., Petrović, J. S., Maluckov, A., Hadžievski, L.,& Malomed, B. A.. (2015). Composite localized modes in discretized spin-orbit-coupled Bose-Einstein condensates. in Journal of Physics. B: Atomic Molecular and Optical Physics, 48(6).
https://doi.org/10.1088/0953-4075/48/6/065301

Beličev P, Gligorić G, Petrović JS, Maluckov A, Hadžievski L, Malomed BA. Composite localized modes in discretized spin-orbit-coupled Bose-Einstein condensates. in Journal of Physics. B: Atomic Molecular and Optical Physics. 2015;48(6).
doi:10.1088/0953-4075/48/6/065301 .

Beličev, Petra, Gligorić, Goran, Petrović, Jovana S., Maluckov, Aleksandra, Hadžievski, Ljupčo, Malomed, Boris A., "Composite localized modes in discretized spin-orbit-coupled Bose-Einstein condensates" in Journal of Physics. B: Atomic Molecular and Optical Physics, 48, no. 6 (2015),
https://doi.org/10.1088/0953-4075/48/6/065301 . .

TY  - JOUR
AU  - Gligorić, Goran
AU  - Maluckov, Aleksandra
AU  - Hadžievski, Ljupčo
AU  - Slepyan, G. Ya
AU  - Malomed, Boris A.
PY  - 2015
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/567
AB  - We consider two-dimensional (2D) arrays of self-organized semiconductor quantum dots (QDs) strongly interacting with electromagnetic field in the regime of Rabi oscillations. The QD array built of two-level states is modelled by two coupled systems of discrete nonlinear Schrodinger equations. Localized modes in the form of single-peaked fundamental and vortical stationary Rabi solitons and self-trapped breathers have been found. The results for the stability, mobility and radiative properties of the Rabi modes suggest a concept of a self-assembled 2D soliton-based nano-antenna, which is stable against imperfections In particular, we discuss the implementation of such a nano-antenna in the form of surface plasmon solitons in graphene, and illustrate possibilities to control their operation by means of optical tools.
T2  - Journal of Physics: Condensed Matter
T1  - Soliton nanoantennas in two-dimensional arrays of quantum dots
VL  - 27
IS  - 22
DO  - 10.1088/0953-8984/27/22/225301
ER  - 

@article{
author = "Gligorić, Goran and Maluckov, Aleksandra and Hadžievski, Ljupčo and Slepyan, G. Ya and Malomed, Boris A.",
year = "2015",
abstract = "We consider two-dimensional (2D) arrays of self-organized semiconductor quantum dots (QDs) strongly interacting with electromagnetic field in the regime of Rabi oscillations. The QD array built of two-level states is modelled by two coupled systems of discrete nonlinear Schrodinger equations. Localized modes in the form of single-peaked fundamental and vortical stationary Rabi solitons and self-trapped breathers have been found. The results for the stability, mobility and radiative properties of the Rabi modes suggest a concept of a self-assembled 2D soliton-based nano-antenna, which is stable against imperfections In particular, we discuss the implementation of such a nano-antenna in the form of surface plasmon solitons in graphene, and illustrate possibilities to control their operation by means of optical tools.",
journal = "Journal of Physics: Condensed Matter",
title = "Soliton nanoantennas in two-dimensional arrays of quantum dots",
volume = "27",
number = "22",
doi = "10.1088/0953-8984/27/22/225301"
}

Gligorić, G., Maluckov, A., Hadžievski, L., Slepyan, G. Y.,& Malomed, B. A.. (2015). Soliton nanoantennas in two-dimensional arrays of quantum dots. in Journal of Physics: Condensed Matter, 27(22).
https://doi.org/10.1088/0953-8984/27/22/225301

Gligorić G, Maluckov A, Hadžievski L, Slepyan GY, Malomed BA. Soliton nanoantennas in two-dimensional arrays of quantum dots. in Journal of Physics: Condensed Matter. 2015;27(22).
doi:10.1088/0953-8984/27/22/225301 .

Gligorić, Goran, Maluckov, Aleksandra, Hadžievski, Ljupčo, Slepyan, G. Ya, Malomed, Boris A., "Soliton nanoantennas in two-dimensional arrays of quantum dots" in Journal of Physics: Condensed Matter, 27, no. 22 (2015),
https://doi.org/10.1088/0953-8984/27/22/225301 . .

TY  - JOUR
AU  - Gligorić, Goran
AU  - Maluckov, Aleksandra
AU  - Hadžievski, Ljupčo
AU  - Malomed, Boris A.
PY  - 2014
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/6065
AB  - Spatially periodic modulation of the intersite coupling in two-dimensional (2D) nonlinear lattices modifies the eigenvalue spectrum by opening mini-gaps in it. This work aims to build stable localized modes in the new bandgaps. Numerical analysis shows that single-peak and composite two-and four-peak discrete static solitons and breathers emerge as such modes in certain parameter areas inside the mini-gaps of the 2D superlattice induced by the periodic modulation of the intersite coupling along both directions. The single-peak solitons and four-peak discrete solitons are stable in a part of their existence domain, while unstable stationary states (in particular, two-soliton complexes) may readily transform into robust localized breathers.
T2  - Chaos
T1  - Localized modes in mini-gaps opened by periodically modulated intersite coupling in two-dimensional nonlinear lattices
VL  - 24
IS  - 2
DO  - 10.1063/1.4881678
ER  - 

@article{
author = "Gligorić, Goran and Maluckov, Aleksandra and Hadžievski, Ljupčo and Malomed, Boris A.",
year = "2014",
abstract = "Spatially periodic modulation of the intersite coupling in two-dimensional (2D) nonlinear lattices modifies the eigenvalue spectrum by opening mini-gaps in it. This work aims to build stable localized modes in the new bandgaps. Numerical analysis shows that single-peak and composite two-and four-peak discrete static solitons and breathers emerge as such modes in certain parameter areas inside the mini-gaps of the 2D superlattice induced by the periodic modulation of the intersite coupling along both directions. The single-peak solitons and four-peak discrete solitons are stable in a part of their existence domain, while unstable stationary states (in particular, two-soliton complexes) may readily transform into robust localized breathers.",
journal = "Chaos",
title = "Localized modes in mini-gaps opened by periodically modulated intersite coupling in two-dimensional nonlinear lattices",
volume = "24",
number = "2",
doi = "10.1063/1.4881678"
}

Gligorić, G., Maluckov, A., Hadžievski, L.,& Malomed, B. A.. (2014). Localized modes in mini-gaps opened by periodically modulated intersite coupling in two-dimensional nonlinear lattices. in Chaos, 24(2).
https://doi.org/10.1063/1.4881678

Gligorić G, Maluckov A, Hadžievski L, Malomed BA. Localized modes in mini-gaps opened by periodically modulated intersite coupling in two-dimensional nonlinear lattices. in Chaos. 2014;24(2).
doi:10.1063/1.4881678 .

Gligorić, Goran, Maluckov, Aleksandra, Hadžievski, Ljupčo, Malomed, Boris A., "Localized modes in mini-gaps opened by periodically modulated intersite coupling in two-dimensional nonlinear lattices" in Chaos, 24, no. 2 (2014),
https://doi.org/10.1063/1.4881678 . .

TY  - JOUR
AU  - Stojanović, Marija
AU  - Petrovic, M. D.
AU  - Gligorić, Goran
AU  - Maluckov, Aleksandra
AU  - Hadžievski, Ljupčo
AU  - Malomed, Boris A.
PY  - 2013
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/7020
AB  - We investigate the stability and dynamical properties of complexes consisting of two identical vortices with topological charges S = 1 and 2 in the system of two linearly on-site-coupled two-dimensional (2D) vortices. The system is mathematically modeled by two coupled nonlinear differential-difference 2D Schrodinger equations. It is found that the on-site and off-site vortices form symmetric and asymmetric complexes, respectively, with respect to the interface sites. In general, the existence regions of complexes shrink with an increase of the interlattice coupling strength. Stable symmetric complexes exist within the stability window in the parametric space whose width gradually shrinks with an increase of the interlattice coupling strength. The asymmetric vortex complexes are unstable, except in the limit of vanishing coupling between lattices.
T2  - Physica Scripta
T1  - Vortex complexes in two-dimensional optical lattices linearly coupled at a single site
VL  - T157
DO  - 10.1088/0031-8949/2013/T157/014030
ER  - 

@article{
author = "Stojanović, Marija and Petrovic, M. D. and Gligorić, Goran and Maluckov, Aleksandra and Hadžievski, Ljupčo and Malomed, Boris A.",
year = "2013",
abstract = "We investigate the stability and dynamical properties of complexes consisting of two identical vortices with topological charges S = 1 and 2 in the system of two linearly on-site-coupled two-dimensional (2D) vortices. The system is mathematically modeled by two coupled nonlinear differential-difference 2D Schrodinger equations. It is found that the on-site and off-site vortices form symmetric and asymmetric complexes, respectively, with respect to the interface sites. In general, the existence regions of complexes shrink with an increase of the interlattice coupling strength. Stable symmetric complexes exist within the stability window in the parametric space whose width gradually shrinks with an increase of the interlattice coupling strength. The asymmetric vortex complexes are unstable, except in the limit of vanishing coupling between lattices.",
journal = "Physica Scripta",
title = "Vortex complexes in two-dimensional optical lattices linearly coupled at a single site",
volume = "T157",
doi = "10.1088/0031-8949/2013/T157/014030"
}

Stojanović, M., Petrovic, M. D., Gligorić, G., Maluckov, A., Hadžievski, L.,& Malomed, B. A.. (2013). Vortex complexes in two-dimensional optical lattices linearly coupled at a single site. in Physica Scripta, T157.
https://doi.org/10.1088/0031-8949/2013/T157/014030

Stojanović M, Petrovic MD, Gligorić G, Maluckov A, Hadžievski L, Malomed BA. Vortex complexes in two-dimensional optical lattices linearly coupled at a single site. in Physica Scripta. 2013;T157.
doi:10.1088/0031-8949/2013/T157/014030 .

Stojanović, Marija, Petrovic, M. D., Gligorić, Goran, Maluckov, Aleksandra, Hadžievski, Ljupčo, Malomed, Boris A., "Vortex complexes in two-dimensional optical lattices linearly coupled at a single site" in Physica Scripta, T157 (2013),
https://doi.org/10.1088/0031-8949/2013/T157/014030 . .

TY  - JOUR
AU  - Maluckov, Aleksandra
AU  - Gligorić, Goran
AU  - Hadžievski, Ljupčo
AU  - Malomed, Boris A.
AU  - Pfau, Tilman
PY  - 2013
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/5319
AB  - We study normal modes propagating on top of the stable uniform background in arrays of dipolar Bose-Einstein condensate (BEC) droplets trapped in a deep optical lattice. Both the on-site mean-field dynamics of the droplets and their displacement due to the repulsive dipole-dipole interactions (DDIs) are taken into account. Dispersion relations for two modes, viz., high-and low-frequency counterparts of optical and acoustic phonon modes in condensed matter, are derived analytically and verified by direct simulations, for both cases of the repulsive and attractive contact interactions. The (counterpart of the) optical-phonon branch does not exist without the DDIs. These results are relevant in the connection to emerging experimental techniques enabling real-time imaging of the condensate dynamics and direct experimental measurement of phonon dispersion relations in BECs. DOI: 10.1103/PhysRevA.87.023623
T2  - Physical Review A
T1  - High- and low-frequency phonon modes in dipolar quantum gases trapped in deep lattices
VL  - 87
IS  - 2
DO  - 10.1103/PhysRevA.87.023623
ER  - 

@article{
author = "Maluckov, Aleksandra and Gligorić, Goran and Hadžievski, Ljupčo and Malomed, Boris A. and Pfau, Tilman",
year = "2013",
abstract = "We study normal modes propagating on top of the stable uniform background in arrays of dipolar Bose-Einstein condensate (BEC) droplets trapped in a deep optical lattice. Both the on-site mean-field dynamics of the droplets and their displacement due to the repulsive dipole-dipole interactions (DDIs) are taken into account. Dispersion relations for two modes, viz., high-and low-frequency counterparts of optical and acoustic phonon modes in condensed matter, are derived analytically and verified by direct simulations, for both cases of the repulsive and attractive contact interactions. The (counterpart of the) optical-phonon branch does not exist without the DDIs. These results are relevant in the connection to emerging experimental techniques enabling real-time imaging of the condensate dynamics and direct experimental measurement of phonon dispersion relations in BECs. DOI: 10.1103/PhysRevA.87.023623",
journal = "Physical Review A",
title = "High- and low-frequency phonon modes in dipolar quantum gases trapped in deep lattices",
volume = "87",
number = "2",
doi = "10.1103/PhysRevA.87.023623"
}

Maluckov, A., Gligorić, G., Hadžievski, L., Malomed, B. A.,& Pfau, T.. (2013). High- and low-frequency phonon modes in dipolar quantum gases trapped in deep lattices. in Physical Review A, 87(2).
https://doi.org/10.1103/PhysRevA.87.023623

Maluckov A, Gligorić G, Hadžievski L, Malomed BA, Pfau T. High- and low-frequency phonon modes in dipolar quantum gases trapped in deep lattices. in Physical Review A. 2013;87(2).
doi:10.1103/PhysRevA.87.023623 .

Maluckov, Aleksandra, Gligorić, Goran, Hadžievski, Ljupčo, Malomed, Boris A., Pfau, Tilman, "High- and low-frequency phonon modes in dipolar quantum gases trapped in deep lattices" in Physical Review A, 87, no. 2 (2013),
https://doi.org/10.1103/PhysRevA.87.023623 . .

TY  - JOUR
AU  - Gligorić, Goran
AU  - Maluckov, Aleksandra
AU  - Hadžievski, Ljupčo
AU  - Malomed, Boris A.
PY  - 2013
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/5667
AB  - We report that infinite and semi-infinite lattices with spatially inhomogeneous self-defocusing (SDF) onsite nonlinearity, whose strength increases rapidly enough toward the lattice periphery, support stable unstaggered (UnST) discrete bright solitons, which do not exist in lattices with the spatially uniform SDF nonlinearity. The UnST solitons coexist with stable staggered (ST) localized modes, which are always possible under the defocusing onsite nonlinearity. The results are obtained in a numerical form and also by means of variational approximation (VA). In the semi-infinite (truncated) system, some solutions for the UnST surface solitons are produced in an exact form. On the contrary to surface discrete solitons in uniform truncated lattices, the threshold value of the norm vanishes for the UnST solitons in the present system. Stability regions for the novel UnST solitons are identified. The same results imply the existence of ST discrete solitons in lattices with the spatially growing self-focusing nonlinearity, where such solitons cannot exist either if the nonlinearity is homogeneous. In addition, a lattice with the uniform onsite SDF nonlinearity and exponentially decaying intersite coupling is introduced and briefly considered. Via a similar mechanism, it may also support UnST discrete solitons. The results may be realized in arrayed optical waveguides and collisionally inhomogeneous Bose-Einstein condensates trapped in deep optical lattices. A generalization for a two-dimensional system is briefly considered.
T2  - Physical Review E
T1  - Discrete localized modes supported by an inhomogeneous defocusing nonlinearity
VL  - 88
IS  - 3
DO  - 10.1103/PhysRevE.88.032905
ER  - 

@article{
author = "Gligorić, Goran and Maluckov, Aleksandra and Hadžievski, Ljupčo and Malomed, Boris A.",
year = "2013",
abstract = "We report that infinite and semi-infinite lattices with spatially inhomogeneous self-defocusing (SDF) onsite nonlinearity, whose strength increases rapidly enough toward the lattice periphery, support stable unstaggered (UnST) discrete bright solitons, which do not exist in lattices with the spatially uniform SDF nonlinearity. The UnST solitons coexist with stable staggered (ST) localized modes, which are always possible under the defocusing onsite nonlinearity. The results are obtained in a numerical form and also by means of variational approximation (VA). In the semi-infinite (truncated) system, some solutions for the UnST surface solitons are produced in an exact form. On the contrary to surface discrete solitons in uniform truncated lattices, the threshold value of the norm vanishes for the UnST solitons in the present system. Stability regions for the novel UnST solitons are identified. The same results imply the existence of ST discrete solitons in lattices with the spatially growing self-focusing nonlinearity, where such solitons cannot exist either if the nonlinearity is homogeneous. In addition, a lattice with the uniform onsite SDF nonlinearity and exponentially decaying intersite coupling is introduced and briefly considered. Via a similar mechanism, it may also support UnST discrete solitons. The results may be realized in arrayed optical waveguides and collisionally inhomogeneous Bose-Einstein condensates trapped in deep optical lattices. A generalization for a two-dimensional system is briefly considered.",
journal = "Physical Review E",
title = "Discrete localized modes supported by an inhomogeneous defocusing nonlinearity",
volume = "88",
number = "3",
doi = "10.1103/PhysRevE.88.032905"
}

Gligorić, G., Maluckov, A., Hadžievski, L.,& Malomed, B. A.. (2013). Discrete localized modes supported by an inhomogeneous defocusing nonlinearity. in Physical Review E, 88(3).
https://doi.org/10.1103/PhysRevE.88.032905

Gligorić G, Maluckov A, Hadžievski L, Malomed BA. Discrete localized modes supported by an inhomogeneous defocusing nonlinearity. in Physical Review E. 2013;88(3).
doi:10.1103/PhysRevE.88.032905 .

Gligorić, Goran, Maluckov, Aleksandra, Hadžievski, Ljupčo, Malomed, Boris A., "Discrete localized modes supported by an inhomogeneous defocusing nonlinearity" in Physical Review E, 88, no. 3 (2013),
https://doi.org/10.1103/PhysRevE.88.032905 . .

TY  - JOUR
AU  - Gligorić, Goran
AU  - Maluckov, Aleksandra
AU  - Hadžievski, Ljupčo
AU  - Slepyan, Gregory Ya.
AU  - Malomed, Boris A.
PY  - 2013
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/5736
AB  - We develop a theory for the interaction of classical light fields within a chain of coupled quantum dots (QDs), in the strong-coupling regime, taking into account the local-field effects. The QD chain is modeled by a one-dimensional periodic array of two-level quantum particles with tunnel coupling between adjacent ones. The local-field effect is taken into regard as QD depolarization in the Hartree-Fock-Bogoliubov approximation. The dynamics of the chain is described by a system of two discrete nonlinear Schrodinger (DNLS) equations for local amplitudes of the probabilities of the ground and first excited states. The two equations are coupled by cross-phase-modulation cubic terms, produced by the local-field action, and by linear terms also. In comparison to previously studied DNLS systems, an essentially new feature is a phase shift between the intersite-hopping constants in the two equations. By means of numerical solutions, we demonstrate that, in this QD chain, Rabi oscillations (RO) self-trap into stable bright Rabi solitons or Rabi breathers. The mobility of the solitons is considered as well. The related behavior of the observable quantities, such as energy, inversion, and electric-current density, is given a physical interpretation. The results apply to a realistic region of physical parameters.
T2  - Physical Review B: Condensed Matter and Materials Physics
T1  - Discrete solitons in an array of quantum dots
VL  - 88
IS  - 15
DO  - 10.1103/PhysRevB.88.155329
ER  - 

@article{
author = "Gligorić, Goran and Maluckov, Aleksandra and Hadžievski, Ljupčo and Slepyan, Gregory Ya. and Malomed, Boris A.",
year = "2013",
abstract = "We develop a theory for the interaction of classical light fields within a chain of coupled quantum dots (QDs), in the strong-coupling regime, taking into account the local-field effects. The QD chain is modeled by a one-dimensional periodic array of two-level quantum particles with tunnel coupling between adjacent ones. The local-field effect is taken into regard as QD depolarization in the Hartree-Fock-Bogoliubov approximation. The dynamics of the chain is described by a system of two discrete nonlinear Schrodinger (DNLS) equations for local amplitudes of the probabilities of the ground and first excited states. The two equations are coupled by cross-phase-modulation cubic terms, produced by the local-field action, and by linear terms also. In comparison to previously studied DNLS systems, an essentially new feature is a phase shift between the intersite-hopping constants in the two equations. By means of numerical solutions, we demonstrate that, in this QD chain, Rabi oscillations (RO) self-trap into stable bright Rabi solitons or Rabi breathers. The mobility of the solitons is considered as well. The related behavior of the observable quantities, such as energy, inversion, and electric-current density, is given a physical interpretation. The results apply to a realistic region of physical parameters.",
journal = "Physical Review B: Condensed Matter and Materials Physics",
title = "Discrete solitons in an array of quantum dots",
volume = "88",
number = "15",
doi = "10.1103/PhysRevB.88.155329"
}

Gligorić, G., Maluckov, A., Hadžievski, L., Slepyan, G. Ya.,& Malomed, B. A.. (2013). Discrete solitons in an array of quantum dots. in Physical Review B: Condensed Matter and Materials Physics, 88(15).
https://doi.org/10.1103/PhysRevB.88.155329

Gligorić G, Maluckov A, Hadžievski L, Slepyan GY, Malomed BA. Discrete solitons in an array of quantum dots. in Physical Review B: Condensed Matter and Materials Physics. 2013;88(15).
doi:10.1103/PhysRevB.88.155329 .

Gligorić, Goran, Maluckov, Aleksandra, Hadžievski, Ljupčo, Slepyan, Gregory Ya., Malomed, Boris A., "Discrete solitons in an array of quantum dots" in Physical Review B: Condensed Matter and Materials Physics, 88, no. 15 (2013),
https://doi.org/10.1103/PhysRevB.88.155329 . .

TY  - JOUR
AU  - Maluckov, Aleksandra
AU  - Gligorić, Goran
AU  - Hadžievski, Ljupčo
AU  - Malomed, Boris A.
AU  - Pfau, Tilman
PY  - 2012
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/4357
AB  - Density-wave patterns in discrete media with local interactions are known to be unstable. We demonstrate that stable double-and triple-period patterns (DPPs and TPPs), with respect to the period of the underlying lattice, exist in media with nonlocal nonlinearity. This is shown in detail for dipolar Bose-Einstein condensates, loaded into a deep one-dimensional optical lattice. The DPP and TPP emerge via phase transitions of the second and first kind, respectively. The emerging patterns may be stable if the dipole-dipole interactions are repulsive and sufficiently strong, in comparison with the local repulsive nonlinearity. Within the set of the considered states, the TPPs realize a minimum of the free energy. Avast stability region for the TPPs is found in the parameter space, while the DPP stability region is relatively narrow. The same mechanism may create stable density-wave patterns in other physical media featuring nonlocal interactions.
T2  - Physical Review Letters
T1  - Stable Periodic Density Waves in Dipolar Bose-Einstein Condensates Trapped in Optical Lattices
VL  - 108
IS  - 14
DO  - 10.1103/PhysRevLett.108.140402
ER  - 

@article{
author = "Maluckov, Aleksandra and Gligorić, Goran and Hadžievski, Ljupčo and Malomed, Boris A. and Pfau, Tilman",
year = "2012",
abstract = "Density-wave patterns in discrete media with local interactions are known to be unstable. We demonstrate that stable double-and triple-period patterns (DPPs and TPPs), with respect to the period of the underlying lattice, exist in media with nonlocal nonlinearity. This is shown in detail for dipolar Bose-Einstein condensates, loaded into a deep one-dimensional optical lattice. The DPP and TPP emerge via phase transitions of the second and first kind, respectively. The emerging patterns may be stable if the dipole-dipole interactions are repulsive and sufficiently strong, in comparison with the local repulsive nonlinearity. Within the set of the considered states, the TPPs realize a minimum of the free energy. Avast stability region for the TPPs is found in the parameter space, while the DPP stability region is relatively narrow. The same mechanism may create stable density-wave patterns in other physical media featuring nonlocal interactions.",
journal = "Physical Review Letters",
title = "Stable Periodic Density Waves in Dipolar Bose-Einstein Condensates Trapped in Optical Lattices",
volume = "108",
number = "14",
doi = "10.1103/PhysRevLett.108.140402"
}

Maluckov, A., Gligorić, G., Hadžievski, L., Malomed, B. A.,& Pfau, T.. (2012). Stable Periodic Density Waves in Dipolar Bose-Einstein Condensates Trapped in Optical Lattices. in Physical Review Letters, 108(14).
https://doi.org/10.1103/PhysRevLett.108.140402

Maluckov A, Gligorić G, Hadžievski L, Malomed BA, Pfau T. Stable Periodic Density Waves in Dipolar Bose-Einstein Condensates Trapped in Optical Lattices. in Physical Review Letters. 2012;108(14).
doi:10.1103/PhysRevLett.108.140402 .

Maluckov, Aleksandra, Gligorić, Goran, Hadžievski, Ljupčo, Malomed, Boris A., Pfau, Tilman, "Stable Periodic Density Waves in Dipolar Bose-Einstein Condensates Trapped in Optical Lattices" in Physical Review Letters, 108, no. 14 (2012),
https://doi.org/10.1103/PhysRevLett.108.140402 . .

TY  - JOUR
AU  - Petrović, M. D.
AU  - Gligorić, Goran
AU  - Maluckov, Aleksandra
AU  - Hadžievski, Ljupčo
AU  - Malomed, Boris A.
PY  - 2011
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/4441
AB  - Existence, stability, and dynamics of soliton complexes, centered at the site of a single transverse link connecting two parallel two-dimensional (2D) lattices, are investigated. The system with the onsite cubic self-focusing nonlinearity is modeled by the pair of discrete nonlinear Schrodinger equations linearly coupled at the single site. Symmetric, antisymmetric, and asymmetric complexes are constructed by means of the variational approximation (VA) and numerical methods. The VA demonstrates that the antisymmetric soliton complexes exist in the entire parameter space, while the symmetric and asymmetric modes can be found below a critical value of the coupling parameter. Numerical results confirm these predictions. The symmetric complexes are destabilized via a supercritical symmetry-breaking pitchfork bifurcation, which gives rise to stable asymmetric modes. The antisymmetric complexes are subject to oscillatory and exponentially instabilities in narrow parametric regions. In bistability areas, stable antisymmetric solitons coexist with either symmetric or asymmetric ones.
T2  - Physical Review E
T1  - Interface solitons in locally linked two-dimensional lattices
VL  - 84
IS  - 2
DO  - 10.1103/PhysRevE.84.026602
ER  - 

@article{
author = "Petrović, M. D. and Gligorić, Goran and Maluckov, Aleksandra and Hadžievski, Ljupčo and Malomed, Boris A.",
year = "2011",
abstract = "Existence, stability, and dynamics of soliton complexes, centered at the site of a single transverse link connecting two parallel two-dimensional (2D) lattices, are investigated. The system with the onsite cubic self-focusing nonlinearity is modeled by the pair of discrete nonlinear Schrodinger equations linearly coupled at the single site. Symmetric, antisymmetric, and asymmetric complexes are constructed by means of the variational approximation (VA) and numerical methods. The VA demonstrates that the antisymmetric soliton complexes exist in the entire parameter space, while the symmetric and asymmetric modes can be found below a critical value of the coupling parameter. Numerical results confirm these predictions. The symmetric complexes are destabilized via a supercritical symmetry-breaking pitchfork bifurcation, which gives rise to stable asymmetric modes. The antisymmetric complexes are subject to oscillatory and exponentially instabilities in narrow parametric regions. In bistability areas, stable antisymmetric solitons coexist with either symmetric or asymmetric ones.",
journal = "Physical Review E",
title = "Interface solitons in locally linked two-dimensional lattices",
volume = "84",
number = "2",
doi = "10.1103/PhysRevE.84.026602"
}

Petrović, M. D., Gligorić, G., Maluckov, A., Hadžievski, L.,& Malomed, B. A.. (2011). Interface solitons in locally linked two-dimensional lattices. in Physical Review E, 84(2).
https://doi.org/10.1103/PhysRevE.84.026602

Petrović MD, Gligorić G, Maluckov A, Hadžievski L, Malomed BA. Interface solitons in locally linked two-dimensional lattices. in Physical Review E. 2011;84(2).
doi:10.1103/PhysRevE.84.026602 .

Petrović, M. D., Gligorić, Goran, Maluckov, Aleksandra, Hadžievski, Ljupčo, Malomed, Boris A., "Interface solitons in locally linked two-dimensional lattices" in Physical Review E, 84, no. 2 (2011),
https://doi.org/10.1103/PhysRevE.84.026602 . .

TY  - JOUR
AU  - Stojanović, Mirjana
AU  - Maluckov, Aleksandra
AU  - Hadžievski, Ljupčo
AU  - Malomed, Boris A.
PY  - 2011
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/4493
AB  - Fundamental solitons pinned to the interface between three semi-infinite one-dimensional nonlinear dynamical chains, coupled at a single site, are investigated. The light propagation in the respective system with the self-attractive on-site cubic nonlinearity, which can be implemented as an array of nonlinear optical waveguides, is modeled by the system of three discrete nonlinear Schrodinger equations. The formation, stability and dynamics of symmetric and asymmetric fundamental solitons centered at the interface are investigated analytically by means of the variational approximation (VA) and in a numerical form. The VA predicts that two asymmetric and two antisymmetric branches exist in the entire parameter space, while four asymmetric modes and the symmetric one can be found below some critical value of the inter-lattice coupling parameter actually, past the symmetry-breaking bifurcation. At this bifurcation point, the symmetric branch is destabilized and two new asymmetric soliton branches appear, one stable and the other unstable. In this area, the antisymmetric branch changes its character, getting stabilized against oscillatory perturbations. In direct simulations, unstable symmetric modes radiate a part of their power, staying trapped around the interface. Highly unstable asymmetric modes transform into localized breathers traveling from the interface region across the lattice without significant power loss. (C) 2011 Elsevier B.V. All rights reserved.
T2  - Physica. D: Nonlinear Phenomena
T1  - Surface solitons in trilete lattices
VL  - 240
IS  - 18
SP  - 1489
EP  - 1496
DO  - 10.1016/j.physd.2011.06.017
ER  - 

@article{
author = "Stojanović, Mirjana and Maluckov, Aleksandra and Hadžievski, Ljupčo and Malomed, Boris A.",
year = "2011",
abstract = "Fundamental solitons pinned to the interface between three semi-infinite one-dimensional nonlinear dynamical chains, coupled at a single site, are investigated. The light propagation in the respective system with the self-attractive on-site cubic nonlinearity, which can be implemented as an array of nonlinear optical waveguides, is modeled by the system of three discrete nonlinear Schrodinger equations. The formation, stability and dynamics of symmetric and asymmetric fundamental solitons centered at the interface are investigated analytically by means of the variational approximation (VA) and in a numerical form. The VA predicts that two asymmetric and two antisymmetric branches exist in the entire parameter space, while four asymmetric modes and the symmetric one can be found below some critical value of the inter-lattice coupling parameter actually, past the symmetry-breaking bifurcation. At this bifurcation point, the symmetric branch is destabilized and two new asymmetric soliton branches appear, one stable and the other unstable. In this area, the antisymmetric branch changes its character, getting stabilized against oscillatory perturbations. In direct simulations, unstable symmetric modes radiate a part of their power, staying trapped around the interface. Highly unstable asymmetric modes transform into localized breathers traveling from the interface region across the lattice without significant power loss. (C) 2011 Elsevier B.V. All rights reserved.",
journal = "Physica. D: Nonlinear Phenomena",
title = "Surface solitons in trilete lattices",
volume = "240",
number = "18",
pages = "1489-1496",
doi = "10.1016/j.physd.2011.06.017"
}

Stojanović, M., Maluckov, A., Hadžievski, L.,& Malomed, B. A.. (2011). Surface solitons in trilete lattices. in Physica. D: Nonlinear Phenomena, 240(18), 1489-1496.
https://doi.org/10.1016/j.physd.2011.06.017

Stojanović M, Maluckov A, Hadžievski L, Malomed BA. Surface solitons in trilete lattices. in Physica. D: Nonlinear Phenomena. 2011;240(18):1489-1496.
doi:10.1016/j.physd.2011.06.017 .

Stojanović, Mirjana, Maluckov, Aleksandra, Hadžievski, Ljupčo, Malomed, Boris A., "Surface solitons in trilete lattices" in Physica. D: Nonlinear Phenomena, 240, no. 18 (2011):1489-1496,
https://doi.org/10.1016/j.physd.2011.06.017 . .

TY  - JOUR
AU  - Gligorić, Goran
AU  - Maluckov, Aleksandra
AU  - Stepić, Milutin
AU  - Hadžievski, Ljupčo
AU  - Malomed, Boris A.
PY  - 2010
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/4117
AB  - We investigate the effects of dipole-dipole (DD) interactions on immiscibility-miscibility transitions (IMTs) in two-component Bose-Einstein condensates (BECs) trapped in the harmonic-oscillator (HO) potential, with the components linearly coupled by a resonant electromagnetic field (accordingly, the components represent two different spin states of the same atom). The problem is studied by means of direct numerical simulations. Different mutual orientations of the dipolar moments in the two components are considered. It is shown that, in the binary BEC formed by dipoles with the same orientation and equal magnitudes, the IMT cannot be induced by the DD interaction alone, being possible only in the presence of the linear coupling between the components, while the miscibility threshold is affected by the DD interactions. However, in the binary condensate with the two dipolar components polarized in opposite directions, the IMT can be induced without any linear coupling. Further, we demonstrate that those miscible and immiscible localized states, formed in the presence of the DD interactions, which are unstable evolve into robust breathers, which tend to keep the original miscibility or immiscibility, respectively. An exception is the case of a very strong DD attraction, when narrow stationary modes are destroyed by the instability. The binary BEC composed of copolarized dipoles with different magnitudes are briefly considered as well.
T2  - Physical Review A
T1  - Transition to miscibility in linearly coupled binary dipolar Bose-Einstein condensates
VL  - 82
IS  - 3
DO  - 10.1103/PhysRevA.82.033624
ER  - 

@article{
author = "Gligorić, Goran and Maluckov, Aleksandra and Stepić, Milutin and Hadžievski, Ljupčo and Malomed, Boris A.",
year = "2010",
abstract = "We investigate the effects of dipole-dipole (DD) interactions on immiscibility-miscibility transitions (IMTs) in two-component Bose-Einstein condensates (BECs) trapped in the harmonic-oscillator (HO) potential, with the components linearly coupled by a resonant electromagnetic field (accordingly, the components represent two different spin states of the same atom). The problem is studied by means of direct numerical simulations. Different mutual orientations of the dipolar moments in the two components are considered. It is shown that, in the binary BEC formed by dipoles with the same orientation and equal magnitudes, the IMT cannot be induced by the DD interaction alone, being possible only in the presence of the linear coupling between the components, while the miscibility threshold is affected by the DD interactions. However, in the binary condensate with the two dipolar components polarized in opposite directions, the IMT can be induced without any linear coupling. Further, we demonstrate that those miscible and immiscible localized states, formed in the presence of the DD interactions, which are unstable evolve into robust breathers, which tend to keep the original miscibility or immiscibility, respectively. An exception is the case of a very strong DD attraction, when narrow stationary modes are destroyed by the instability. The binary BEC composed of copolarized dipoles with different magnitudes are briefly considered as well.",
journal = "Physical Review A",
title = "Transition to miscibility in linearly coupled binary dipolar Bose-Einstein condensates",
volume = "82",
number = "3",
doi = "10.1103/PhysRevA.82.033624"
}

Gligorić, G., Maluckov, A., Stepić, M., Hadžievski, L.,& Malomed, B. A.. (2010). Transition to miscibility in linearly coupled binary dipolar Bose-Einstein condensates. in Physical Review A, 82(3).
https://doi.org/10.1103/PhysRevA.82.033624

Gligorić G, Maluckov A, Stepić M, Hadžievski L, Malomed BA. Transition to miscibility in linearly coupled binary dipolar Bose-Einstein condensates. in Physical Review A. 2010;82(3).
doi:10.1103/PhysRevA.82.033624 .

Gligorić, Goran, Maluckov, Aleksandra, Stepić, Milutin, Hadžievski, Ljupčo, Malomed, Boris A., "Transition to miscibility in linearly coupled binary dipolar Bose-Einstein condensates" in Physical Review A, 82, no. 3 (2010),
https://doi.org/10.1103/PhysRevA.82.033624 . .

TY  - JOUR
AU  - Gligorić, Goran
AU  - Maluckov, Aleksandra
AU  - Stepić, Milutin
AU  - Hadžievski, Ljupčo
AU  - Malomed, Boris A.
PY  - 2010
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/4006
AB  - We analyze the formation and dynamics of bright unstaggered solitons in the disk-shaped dipolar Bose-Einstein condensate, which features the interplay of contact (collisional) and long-range dipole-dipole (DD) interactions between atoms. The condensate is assumed to be trapped in a strong optical-lattice potential in the disks plane, hence it may be approximated by a two-dimensional (2D) discrete model, which includes the on-site nonlinearity and cubic long-range (DD) interactions between sites of the lattice. We consider two such models, which differ by the form of the on-site nonlinearity, represented by the usual cubic term, or more accurate nonpolynomial one, derived from the underlying three-dimensional Gross-Pitaevskii equation. Similar results are obtained for both models. The analysis is focused on the effects of the DD interaction on fundamental localized modes in the lattice (2D discrete solitons). The repulsive isotropic DD nonlinearity extends the existence and stability regions of the fundamental solitons. New families of on-site, inter-site, and hybrid solitons, built on top of a finite background, are found as a result of the interplay of the isotropic repulsive DD interaction and attractive contact nonlinearity. By themselves, these solutions are unstable, but they evolve into robust breathers which exist on an oscillating background. In the presence of the repulsive contact interactions, fundamental localized modes exist if the DD interaction (attractive isotropic or anisotropic) is strong enough. They are stable in narrow regions close to the anticontinuum limit, while unstable solitons evolve into breathers. In the latter case, the presence of the background is immaterial.
T2  - Physical Review A
T1  - Two-dimensional discrete solitons in dipolar Bose-Einstein condensates
VL  - 81
IS  - 1
DO  - 10.1103/PhysRevA.81.013633
ER  - 

@article{
author = "Gligorić, Goran and Maluckov, Aleksandra and Stepić, Milutin and Hadžievski, Ljupčo and Malomed, Boris A.",
year = "2010",
abstract = "We analyze the formation and dynamics of bright unstaggered solitons in the disk-shaped dipolar Bose-Einstein condensate, which features the interplay of contact (collisional) and long-range dipole-dipole (DD) interactions between atoms. The condensate is assumed to be trapped in a strong optical-lattice potential in the disks plane, hence it may be approximated by a two-dimensional (2D) discrete model, which includes the on-site nonlinearity and cubic long-range (DD) interactions between sites of the lattice. We consider two such models, which differ by the form of the on-site nonlinearity, represented by the usual cubic term, or more accurate nonpolynomial one, derived from the underlying three-dimensional Gross-Pitaevskii equation. Similar results are obtained for both models. The analysis is focused on the effects of the DD interaction on fundamental localized modes in the lattice (2D discrete solitons). The repulsive isotropic DD nonlinearity extends the existence and stability regions of the fundamental solitons. New families of on-site, inter-site, and hybrid solitons, built on top of a finite background, are found as a result of the interplay of the isotropic repulsive DD interaction and attractive contact nonlinearity. By themselves, these solutions are unstable, but they evolve into robust breathers which exist on an oscillating background. In the presence of the repulsive contact interactions, fundamental localized modes exist if the DD interaction (attractive isotropic or anisotropic) is strong enough. They are stable in narrow regions close to the anticontinuum limit, while unstable solitons evolve into breathers. In the latter case, the presence of the background is immaterial.",
journal = "Physical Review A",
title = "Two-dimensional discrete solitons in dipolar Bose-Einstein condensates",
volume = "81",
number = "1",
doi = "10.1103/PhysRevA.81.013633"
}

Gligorić, G., Maluckov, A., Stepić, M., Hadžievski, L.,& Malomed, B. A.. (2010). Two-dimensional discrete solitons in dipolar Bose-Einstein condensates. in Physical Review A, 81(1).
https://doi.org/10.1103/PhysRevA.81.013633

Gligorić G, Maluckov A, Stepić M, Hadžievski L, Malomed BA. Two-dimensional discrete solitons in dipolar Bose-Einstein condensates. in Physical Review A. 2010;81(1).
doi:10.1103/PhysRevA.81.013633 .

Gligorić, Goran, Maluckov, Aleksandra, Stepić, Milutin, Hadžievski, Ljupčo, Malomed, Boris A., "Two-dimensional discrete solitons in dipolar Bose-Einstein condensates" in Physical Review A, 81, no. 1 (2010),
https://doi.org/10.1103/PhysRevA.81.013633 . .

TY  - JOUR
AU  - Gligorić, Goran
AU  - Maluckov, Aleksandra
AU  - Stepić, Milutin
AU  - Hadžievski, Ljupčo
AU  - Malomed, Boris A.
PY  - 2010
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/3913
AB  - We analyse the existence, stability and dynamics of localized discrete modes with intrinsic vorticity S = 1 and S = 2 in the disc-shaped dipolar Bose-Einstein condensate loaded into a deep two-dimensional optical lattice. The condensate, which features the interplay of local contact and nonlocal dipole-dipole (DD) interactions between atoms, is modelled by the 2D discrete Gross-Pitaevskii equation which includes the long-range DD term. Various species of discrete vortex solitons, which are known in the model of the condensate with local interactions, are found to exist in the presence of the DD interaction too. In locally self-attractive condensates, the isotropic DD repulsion, which corresponds to the orientation of atomic dipoles perpendicular to the confinement plane, helps to extend the region of the vortex stability, while in the case of anisotropic DD interactions, corresponding to the in-plane orientation of the dipoles, vortices are unstable. In the former case, those vortices which are unstable may evolve into robust ring-shaped breathers. The attractive isotropic DD interaction can create localized vortices in the condensate with the local self-repulsion, but they all are unstable, evolving into single-peak asymmetric structures.
T2  - Journal of Physics. B: Atomic Molecular and Optical Physics
T1  - Discrete vortex solitons in dipolar Bose-Einstein condensates
VL  - 43
IS  - 5
DO  - 10.1088/0953-4075/43/5/055303
ER  - 

@article{
author = "Gligorić, Goran and Maluckov, Aleksandra and Stepić, Milutin and Hadžievski, Ljupčo and Malomed, Boris A.",
year = "2010",
abstract = "We analyse the existence, stability and dynamics of localized discrete modes with intrinsic vorticity S = 1 and S = 2 in the disc-shaped dipolar Bose-Einstein condensate loaded into a deep two-dimensional optical lattice. The condensate, which features the interplay of local contact and nonlocal dipole-dipole (DD) interactions between atoms, is modelled by the 2D discrete Gross-Pitaevskii equation which includes the long-range DD term. Various species of discrete vortex solitons, which are known in the model of the condensate with local interactions, are found to exist in the presence of the DD interaction too. In locally self-attractive condensates, the isotropic DD repulsion, which corresponds to the orientation of atomic dipoles perpendicular to the confinement plane, helps to extend the region of the vortex stability, while in the case of anisotropic DD interactions, corresponding to the in-plane orientation of the dipoles, vortices are unstable. In the former case, those vortices which are unstable may evolve into robust ring-shaped breathers. The attractive isotropic DD interaction can create localized vortices in the condensate with the local self-repulsion, but they all are unstable, evolving into single-peak asymmetric structures.",
journal = "Journal of Physics. B: Atomic Molecular and Optical Physics",
title = "Discrete vortex solitons in dipolar Bose-Einstein condensates",
volume = "43",
number = "5",
doi = "10.1088/0953-4075/43/5/055303"
}

Gligorić, G., Maluckov, A., Stepić, M., Hadžievski, L.,& Malomed, B. A.. (2010). Discrete vortex solitons in dipolar Bose-Einstein condensates. in Journal of Physics. B: Atomic Molecular and Optical Physics, 43(5).
https://doi.org/10.1088/0953-4075/43/5/055303

Gligorić G, Maluckov A, Stepić M, Hadžievski L, Malomed BA. Discrete vortex solitons in dipolar Bose-Einstein condensates. in Journal of Physics. B: Atomic Molecular and Optical Physics. 2010;43(5).
doi:10.1088/0953-4075/43/5/055303 .

Gligorić, Goran, Maluckov, Aleksandra, Stepić, Milutin, Hadžievski, Ljupčo, Malomed, Boris A., "Discrete vortex solitons in dipolar Bose-Einstein condensates" in Journal of Physics. B: Atomic Molecular and Optical Physics, 43, no. 5 (2010),
https://doi.org/10.1088/0953-4075/43/5/055303 . .

TY  - JOUR
AU  - Hadžievski, Ljupčo
AU  - Gligorić, Goran
AU  - Maluckov, Aleksandra
AU  - Malomed, Boris A.
PY  - 2010
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/4099
AB  - Fundamental solitons pinned to the interface between two discrete lattices coupled at a single site are investigated. Serially and parallel-coupled identical chains (system 1 and system 2), with self-attractive on-site cubic nonlinearity, are considered in one dimension. In these two systems, which can be readily implemented as arrays of nonlinear optical waveguides, symmetric, antisymmetric, and asymmetric solitons are investigated by means of the variational approximation (VA) and numerical methods. The VA demonstrates that the antisymmetric solitons exist in the entire parameter space, while the symmetric and asymmetric modes can be found below some critical value of the coupling parameter. Numerical results confirm these predictions for the symmetric and asymmetric fundamental modes. The existence region of numerically found antisymmetric solitons is also limited by a certain value of the coupling parameter. The symmetric solitons are destabilized via a supercritical symmetry-breaking pitchfork bifurcation, which gives rise to stable asymmetric solitons, in both systems. The antisymmetric fundamental solitons, which may be stable or not, do not undergo any bifurcation. In bistability regions, stable antisymmetric solitons coexist with either symmetric or asymmetric solitons.
T2  - Physical Review A
T1  - Interface solitons in one-dimensional locally coupled lattice systems
VL  - 82
IS  - 3
DO  - 10.1103/PhysRevA.82.033806
ER  - 

@article{
author = "Hadžievski, Ljupčo and Gligorić, Goran and Maluckov, Aleksandra and Malomed, Boris A.",
year = "2010",
abstract = "Fundamental solitons pinned to the interface between two discrete lattices coupled at a single site are investigated. Serially and parallel-coupled identical chains (system 1 and system 2), with self-attractive on-site cubic nonlinearity, are considered in one dimension. In these two systems, which can be readily implemented as arrays of nonlinear optical waveguides, symmetric, antisymmetric, and asymmetric solitons are investigated by means of the variational approximation (VA) and numerical methods. The VA demonstrates that the antisymmetric solitons exist in the entire parameter space, while the symmetric and asymmetric modes can be found below some critical value of the coupling parameter. Numerical results confirm these predictions for the symmetric and asymmetric fundamental modes. The existence region of numerically found antisymmetric solitons is also limited by a certain value of the coupling parameter. The symmetric solitons are destabilized via a supercritical symmetry-breaking pitchfork bifurcation, which gives rise to stable asymmetric solitons, in both systems. The antisymmetric fundamental solitons, which may be stable or not, do not undergo any bifurcation. In bistability regions, stable antisymmetric solitons coexist with either symmetric or asymmetric solitons.",
journal = "Physical Review A",
title = "Interface solitons in one-dimensional locally coupled lattice systems",
volume = "82",
number = "3",
doi = "10.1103/PhysRevA.82.033806"
}

Hadžievski, L., Gligorić, G., Maluckov, A.,& Malomed, B. A.. (2010). Interface solitons in one-dimensional locally coupled lattice systems. in Physical Review A, 82(3).
https://doi.org/10.1103/PhysRevA.82.033806

Hadžievski L, Gligorić G, Maluckov A, Malomed BA. Interface solitons in one-dimensional locally coupled lattice systems. in Physical Review A. 2010;82(3).
doi:10.1103/PhysRevA.82.033806 .

Hadžievski, Ljupčo, Gligorić, Goran, Maluckov, Aleksandra, Malomed, Boris A., "Interface solitons in one-dimensional locally coupled lattice systems" in Physical Review A, 82, no. 3 (2010),
https://doi.org/10.1103/PhysRevA.82.033806 . .

TY  - JOUR
AU  - Maluckov, Aleksandra
AU  - Hadžievski, Ljupčo
AU  - Malomed, Boris A.
PY  - 2010
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/4181
AB  - The formation of unstaggered localized modes in dynamical lattices can be supported by the interplay of discreteness and nonlinearity with a finite relaxation time. In rapidly responding nonlinear media, on-site discrete solitons are stable, and their broad intersite counterparts are marginally stable, featuring a virtually vanishing real instability eigenvalue. The solitons become unstable in the case of the slowly relaxing nonlinearity. The character of the instability alters with the increase of the delay time, which leads to a change in the dynamics of unstable discrete solitons. They form robust localized breathers in rapidly relaxing media, and decay into oscillatory diffractive pattern in the lattices with a slow nonlinear response. Marginally stable solitons can freely move across the lattice.
T2  - Chaos
T1  - Fundamental solitons in discrete lattices with a delayed nonlinear response
VL  - 20
IS  - 4
DO  - 10.1063/1.3493407
ER  - 

@article{
author = "Maluckov, Aleksandra and Hadžievski, Ljupčo and Malomed, Boris A.",
year = "2010",
abstract = "The formation of unstaggered localized modes in dynamical lattices can be supported by the interplay of discreteness and nonlinearity with a finite relaxation time. In rapidly responding nonlinear media, on-site discrete solitons are stable, and their broad intersite counterparts are marginally stable, featuring a virtually vanishing real instability eigenvalue. The solitons become unstable in the case of the slowly relaxing nonlinearity. The character of the instability alters with the increase of the delay time, which leads to a change in the dynamics of unstable discrete solitons. They form robust localized breathers in rapidly relaxing media, and decay into oscillatory diffractive pattern in the lattices with a slow nonlinear response. Marginally stable solitons can freely move across the lattice.",
journal = "Chaos",
title = "Fundamental solitons in discrete lattices with a delayed nonlinear response",
volume = "20",
number = "4",
doi = "10.1063/1.3493407"
}

Maluckov, A., Hadžievski, L.,& Malomed, B. A.. (2010). Fundamental solitons in discrete lattices with a delayed nonlinear response. in Chaos, 20(4).
https://doi.org/10.1063/1.3493407

Maluckov A, Hadžievski L, Malomed BA. Fundamental solitons in discrete lattices with a delayed nonlinear response. in Chaos. 2010;20(4).
doi:10.1063/1.3493407 .

Maluckov, Aleksandra, Hadžievski, Ljupčo, Malomed, Boris A., "Fundamental solitons in discrete lattices with a delayed nonlinear response" in Chaos, 20, no. 4 (2010),
https://doi.org/10.1063/1.3493407 . .

TY  - JOUR
AU  - Gligorić, Goran
AU  - Maluckov, Aleksandra
AU  - Hadžievski, Ljupčo
AU  - Malomed, Boris A.
PY  - 2009
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/3711
AB  - The stability and collapse of fundamental unstaggered bright solitons in the discrete Schrodinger equation with the nonpolynomial on-site nonlinearity, which models a nearly one-dimensional Bose-Einstein condensate trapped in a deep optical lattice, are studied in the presence of the long-range dipole-dipole (DD) interactions. The cases of both attractive and repulsive contact and DD interaction are considered. The results are summarized in the form of stability-collapse diagrams in the parametric space of the model, which demonstrate that the attractive DD interactions stabilize the solitons and help to prevent the collapse. Mobility of the discrete solitons is briefly considered too.
T2  - Physical Review A
T1  - Soliton stability and collapse in the discrete nonpolynomial Schrodinger equation with dipole-dipole interactions
VL  - 79
IS  - 5
DO  - 10.1103/PhysRevA.79.053609
ER  - 

@article{
author = "Gligorić, Goran and Maluckov, Aleksandra and Hadžievski, Ljupčo and Malomed, Boris A.",
year = "2009",
abstract = "The stability and collapse of fundamental unstaggered bright solitons in the discrete Schrodinger equation with the nonpolynomial on-site nonlinearity, which models a nearly one-dimensional Bose-Einstein condensate trapped in a deep optical lattice, are studied in the presence of the long-range dipole-dipole (DD) interactions. The cases of both attractive and repulsive contact and DD interaction are considered. The results are summarized in the form of stability-collapse diagrams in the parametric space of the model, which demonstrate that the attractive DD interactions stabilize the solitons and help to prevent the collapse. Mobility of the discrete solitons is briefly considered too.",
journal = "Physical Review A",
title = "Soliton stability and collapse in the discrete nonpolynomial Schrodinger equation with dipole-dipole interactions",
volume = "79",
number = "5",
doi = "10.1103/PhysRevA.79.053609"
}

Gligorić, G., Maluckov, A., Hadžievski, L.,& Malomed, B. A.. (2009). Soliton stability and collapse in the discrete nonpolynomial Schrodinger equation with dipole-dipole interactions. in Physical Review A, 79(5).
https://doi.org/10.1103/PhysRevA.79.053609

Gligorić G, Maluckov A, Hadžievski L, Malomed BA. Soliton stability and collapse in the discrete nonpolynomial Schrodinger equation with dipole-dipole interactions. in Physical Review A. 2009;79(5).
doi:10.1103/PhysRevA.79.053609 .

Gligorić, Goran, Maluckov, Aleksandra, Hadžievski, Ljupčo, Malomed, Boris A., "Soliton stability and collapse in the discrete nonpolynomial Schrodinger equation with dipole-dipole interactions" in Physical Review A, 79, no. 5 (2009),
https://doi.org/10.1103/PhysRevA.79.053609 . .

TY  - JOUR
AU  - Gligorić, Goran
AU  - Maluckov, Aleksandra
AU  - Hadžievski, Ljupčo
AU  - Malomed, Boris A.
PY  - 2009
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/3742
AB  - A model of the Bose-Einstein condensate (BEC) of dipolar atoms, confined in a combination of a cigar-shaped trap and optical lattice acting in the axial direction, is studied in the framework of the one-dimensional (1D) nonpolynomial Schrodinger equation (NPSE) with additional terms describing long-range dipole-dipole (DD) interactions. The NPSE makes it possible to describe the collapse of localized modes, which was experimentally observed in the self-attractive BEC confined in tight traps, in the framework of the 1D description. We study the influence of the DD interactions on the dynamics of bright solitons, especially concerning their collapse-induced instability. Both attractive and repulsive contact and DD interactions are considered. The results are summarized in the form of stability/collapse diagrams in a respective parametric space. In particular, it is shown that the attractive DD interactions may prevent the collapse instability in the condensate with attractive contact interactions.
T2  - Journal of Physics. B: Atomic Molecular and Optical Physics
T1  - Collapse instability of solitons in the nonpolynomial Schrodinger equation with dipole-dipole interactions
VL  - 42
IS  - 14
DO  - 10.1088/0953-4075/42/14/145302
ER  - 

@article{
author = "Gligorić, Goran and Maluckov, Aleksandra and Hadžievski, Ljupčo and Malomed, Boris A.",
year = "2009",
abstract = "A model of the Bose-Einstein condensate (BEC) of dipolar atoms, confined in a combination of a cigar-shaped trap and optical lattice acting in the axial direction, is studied in the framework of the one-dimensional (1D) nonpolynomial Schrodinger equation (NPSE) with additional terms describing long-range dipole-dipole (DD) interactions. The NPSE makes it possible to describe the collapse of localized modes, which was experimentally observed in the self-attractive BEC confined in tight traps, in the framework of the 1D description. We study the influence of the DD interactions on the dynamics of bright solitons, especially concerning their collapse-induced instability. Both attractive and repulsive contact and DD interactions are considered. The results are summarized in the form of stability/collapse diagrams in a respective parametric space. In particular, it is shown that the attractive DD interactions may prevent the collapse instability in the condensate with attractive contact interactions.",
journal = "Journal of Physics. B: Atomic Molecular and Optical Physics",
title = "Collapse instability of solitons in the nonpolynomial Schrodinger equation with dipole-dipole interactions",
volume = "42",
number = "14",
doi = "10.1088/0953-4075/42/14/145302"
}

Gligorić, G., Maluckov, A., Hadžievski, L.,& Malomed, B. A.. (2009). Collapse instability of solitons in the nonpolynomial Schrodinger equation with dipole-dipole interactions. in Journal of Physics. B: Atomic Molecular and Optical Physics, 42(14).
https://doi.org/10.1088/0953-4075/42/14/145302

Gligorić G, Maluckov A, Hadžievski L, Malomed BA. Collapse instability of solitons in the nonpolynomial Schrodinger equation with dipole-dipole interactions. in Journal of Physics. B: Atomic Molecular and Optical Physics. 2009;42(14).
doi:10.1088/0953-4075/42/14/145302 .

Gligorić, Goran, Maluckov, Aleksandra, Hadžievski, Ljupčo, Malomed, Boris A., "Collapse instability of solitons in the nonpolynomial Schrodinger equation with dipole-dipole interactions" in Journal of Physics. B: Atomic Molecular and Optical Physics, 42, no. 14 (2009),
https://doi.org/10.1088/0953-4075/42/14/145302 . .

TY  - JOUR
AU  - Gligorić, Goran
AU  - Maluckov, Aleksandra
AU  - Salasnich, Luca
AU  - Malomed, Boris A.
AU  - Hadžievski, Ljupčo
PY  - 2009
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/3866
AB  - The Bose-Einstein condensate (BEC), confined in a combination of the cigar-shaped trap and axial optical lattice, is studied in the framework of two models described by two versions of the one-dimensional (1D) discrete nonpolynomial Schrodinger equation (NPSE). Both models are derived from the three-dimensional Gross-Pitaevskii equation (3D GPE). To produce model 1 (which was derived in recent works), the 3D GPE is first reduced to the 1D continual NPSE, which is subsequently discretized. Model 2, which was not considered before, is derived by first discretizing the 3D GPE, which is followed by the reduction in the dimension. The two models seem very different; in particular, model 1 is represented by a single discrete equation for the 1D wave function, while model 2 includes an additional equation for the transverse width. Nevertheless, numerical analyses show similar behaviors of fundamental unstaggered solitons in both systems, as concerns their existence region and stability limits. Both models admit the collapse of the localized modes, reproducing the fundamental property of the self-attractive BEC confined in tight traps. Thus, we conclude that the fundamental properties of discrete solitons predicted for the strongly trapped self-attracting BEC are reliable, as the two distinct models produce them in a nearly identical form. However, a difference between the models is found too, as strongly pinned (very narrow) discrete solitons, which were previously found in model 1, are not generated by model 2-in fact, in agreement with the continual 1D NPSE, which does not have such solutions either. In that respect, the newly derived model provides for a more accurate approximation for the trapped BEC.
T2  - Chaos
T1  - Two routes to the one-dimensional discrete nonpolynomial Schrodinger equation
VL  - 19
IS  - 4
DO  - 10.1063/1.3248269
ER  - 

@article{
author = "Gligorić, Goran and Maluckov, Aleksandra and Salasnich, Luca and Malomed, Boris A. and Hadžievski, Ljupčo",
year = "2009",
abstract = "The Bose-Einstein condensate (BEC), confined in a combination of the cigar-shaped trap and axial optical lattice, is studied in the framework of two models described by two versions of the one-dimensional (1D) discrete nonpolynomial Schrodinger equation (NPSE). Both models are derived from the three-dimensional Gross-Pitaevskii equation (3D GPE). To produce model 1 (which was derived in recent works), the 3D GPE is first reduced to the 1D continual NPSE, which is subsequently discretized. Model 2, which was not considered before, is derived by first discretizing the 3D GPE, which is followed by the reduction in the dimension. The two models seem very different; in particular, model 1 is represented by a single discrete equation for the 1D wave function, while model 2 includes an additional equation for the transverse width. Nevertheless, numerical analyses show similar behaviors of fundamental unstaggered solitons in both systems, as concerns their existence region and stability limits. Both models admit the collapse of the localized modes, reproducing the fundamental property of the self-attractive BEC confined in tight traps. Thus, we conclude that the fundamental properties of discrete solitons predicted for the strongly trapped self-attracting BEC are reliable, as the two distinct models produce them in a nearly identical form. However, a difference between the models is found too, as strongly pinned (very narrow) discrete solitons, which were previously found in model 1, are not generated by model 2-in fact, in agreement with the continual 1D NPSE, which does not have such solutions either. In that respect, the newly derived model provides for a more accurate approximation for the trapped BEC.",
journal = "Chaos",
title = "Two routes to the one-dimensional discrete nonpolynomial Schrodinger equation",
volume = "19",
number = "4",
doi = "10.1063/1.3248269"
}

Gligorić, G., Maluckov, A., Salasnich, L., Malomed, B. A.,& Hadžievski, L.. (2009). Two routes to the one-dimensional discrete nonpolynomial Schrodinger equation. in Chaos, 19(4).
https://doi.org/10.1063/1.3248269

Gligorić G, Maluckov A, Salasnich L, Malomed BA, Hadžievski L. Two routes to the one-dimensional discrete nonpolynomial Schrodinger equation. in Chaos. 2009;19(4).
doi:10.1063/1.3248269 .

Gligorić, Goran, Maluckov, Aleksandra, Salasnich, Luca, Malomed, Boris A., Hadžievski, Ljupčo, "Two routes to the one-dimensional discrete nonpolynomial Schrodinger equation" in Chaos, 19, no. 4 (2009),
https://doi.org/10.1063/1.3248269 . .

TY  - JOUR
AU  - Gligorić, Goran
AU  - Maluckov, Aleksandra
AU  - Hadžievski, Ljupčo
AU  - Malomed, Boris A.
PY  - 2008
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/3609
AB  - A model of the Bose-Einstein condensate of dipolar atoms, confined in a combination of a cigar-shaped trap and deep optical lattice acting in the axial direction, is introduced, taking into regard the dipole-dipole (DD) and contact interactions. The model is based on the discrete nonlinear Schrodinger equation with an additional nonlocal term accounting for the DD interactions. The existence and stability of fundamental unstaggered solitons are studied for attractive and repulsive signs of both the local and nonlocal interactions. The DD forces strongly affect the shape and stability of on-site and intersite discrete solitons. The corresponding existence and stability regions in the parametric space are summarized in the form of diagrams, which feature a multiple stability exchange between the on-site and intersite families; in the limit of the dominating DD attraction, the on-site solitons are stable, while their intersite counterparts are not. We also demonstrate that the DD interactions reduce the Peierls-Nabarro barrier and enhance the mobility of the discrete solitons.
T2  - Physical Review A
T1  - Bright solitons in the one-dimensional discrete Gross-Pitaevskii equation with dipole-dipole interactions
VL  - 78
IS  - 6
DO  - 10.1103/PhysRevA.78.063615
ER  - 

@article{
author = "Gligorić, Goran and Maluckov, Aleksandra and Hadžievski, Ljupčo and Malomed, Boris A.",
year = "2008",
abstract = "A model of the Bose-Einstein condensate of dipolar atoms, confined in a combination of a cigar-shaped trap and deep optical lattice acting in the axial direction, is introduced, taking into regard the dipole-dipole (DD) and contact interactions. The model is based on the discrete nonlinear Schrodinger equation with an additional nonlocal term accounting for the DD interactions. The existence and stability of fundamental unstaggered solitons are studied for attractive and repulsive signs of both the local and nonlocal interactions. The DD forces strongly affect the shape and stability of on-site and intersite discrete solitons. The corresponding existence and stability regions in the parametric space are summarized in the form of diagrams, which feature a multiple stability exchange between the on-site and intersite families; in the limit of the dominating DD attraction, the on-site solitons are stable, while their intersite counterparts are not. We also demonstrate that the DD interactions reduce the Peierls-Nabarro barrier and enhance the mobility of the discrete solitons.",
journal = "Physical Review A",
title = "Bright solitons in the one-dimensional discrete Gross-Pitaevskii equation with dipole-dipole interactions",
volume = "78",
number = "6",
doi = "10.1103/PhysRevA.78.063615"
}

Gligorić, G., Maluckov, A., Hadžievski, L.,& Malomed, B. A.. (2008). Bright solitons in the one-dimensional discrete Gross-Pitaevskii equation with dipole-dipole interactions. in Physical Review A, 78(6).
https://doi.org/10.1103/PhysRevA.78.063615

Gligorić G, Maluckov A, Hadžievski L, Malomed BA. Bright solitons in the one-dimensional discrete Gross-Pitaevskii equation with dipole-dipole interactions. in Physical Review A. 2008;78(6).
doi:10.1103/PhysRevA.78.063615 .

Gligorić, Goran, Maluckov, Aleksandra, Hadžievski, Ljupčo, Malomed, Boris A., "Bright solitons in the one-dimensional discrete Gross-Pitaevskii equation with dipole-dipole interactions" in Physical Review A, 78, no. 6 (2008),
https://doi.org/10.1103/PhysRevA.78.063615 . .

TY  - JOUR
AU  - Maluckov, Aleksandra
AU  - Hadžievski, Ljupčo
AU  - Malomed, Boris A.
AU  - Salasnich, Luca
PY  - 2008
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/3502
AB  - We introduce a species of the discrete nonlinear Schrodinger (DNLS) equation, which is a model for a self-attractive Bose-Einstein condensate confined in a combination of a cigar-shaped trap and deep optical lattice acting in the axial direction. The equation is derived as a discretization of the respective nonlinear nonpolynomial Schrodinger equation. Unlike previously considered varieties of one-dimensional DNLS equations, the present discrete model admits on-site collapse. We find two families of unstaggered on-site-centered discrete solitons, stable and unstable ones, which include, respectively, broad and narrow solitons, their stability exactly complying with the Vakhitov-Kolokolov criterion. Unstable on-site solitons either decay or transform themselves into robust breathers. Intersite-centered unstaggered solitons are unstable to collapse; however, they may be stabilized by the application of a sufficiently strong kick, which turns them into moving localized modes. Persistently moving solitons can be readily created too by the application of the kick to stable on-site unstaggered solitons. In the same model, staggered solitons, which are counterparts of gap solitons in the continuum medium, are possible if the intrinsic nonlinearity is self-repulsive. All on-site staggered solitons are stable, while intersite ones have a small instability region. The staggered solitons are immobile.
T2  - Physical Review A
T1  - Solitons in the discrete nonpolynomial Schrodinger equation
VL  - 78
IS  - 1
DO  - 10.1103/PhysRevA.78.013616
ER  - 

@article{
author = "Maluckov, Aleksandra and Hadžievski, Ljupčo and Malomed, Boris A. and Salasnich, Luca",
year = "2008",
abstract = "We introduce a species of the discrete nonlinear Schrodinger (DNLS) equation, which is a model for a self-attractive Bose-Einstein condensate confined in a combination of a cigar-shaped trap and deep optical lattice acting in the axial direction. The equation is derived as a discretization of the respective nonlinear nonpolynomial Schrodinger equation. Unlike previously considered varieties of one-dimensional DNLS equations, the present discrete model admits on-site collapse. We find two families of unstaggered on-site-centered discrete solitons, stable and unstable ones, which include, respectively, broad and narrow solitons, their stability exactly complying with the Vakhitov-Kolokolov criterion. Unstable on-site solitons either decay or transform themselves into robust breathers. Intersite-centered unstaggered solitons are unstable to collapse; however, they may be stabilized by the application of a sufficiently strong kick, which turns them into moving localized modes. Persistently moving solitons can be readily created too by the application of the kick to stable on-site unstaggered solitons. In the same model, staggered solitons, which are counterparts of gap solitons in the continuum medium, are possible if the intrinsic nonlinearity is self-repulsive. All on-site staggered solitons are stable, while intersite ones have a small instability region. The staggered solitons are immobile.",
journal = "Physical Review A",
title = "Solitons in the discrete nonpolynomial Schrodinger equation",
volume = "78",
number = "1",
doi = "10.1103/PhysRevA.78.013616"
}

Maluckov, A., Hadžievski, L., Malomed, B. A.,& Salasnich, L.. (2008). Solitons in the discrete nonpolynomial Schrodinger equation. in Physical Review A, 78(1).
https://doi.org/10.1103/PhysRevA.78.013616

Maluckov A, Hadžievski L, Malomed BA, Salasnich L. Solitons in the discrete nonpolynomial Schrodinger equation. in Physical Review A. 2008;78(1).
doi:10.1103/PhysRevA.78.013616 .

Maluckov, Aleksandra, Hadžievski, Ljupčo, Malomed, Boris A., Salasnich, Luca, "Solitons in the discrete nonpolynomial Schrodinger equation" in Physical Review A, 78, no. 1 (2008),
https://doi.org/10.1103/PhysRevA.78.013616 . .

TY  - JOUR
AU  - Maluckov, Aleksandra
AU  - Hadžievski, Ljupčo
AU  - Malomed, Boris A.
PY  - 2008
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/3398
AB  - Results of a comprehensive dynamical analysis are reported for several fundamental species of bright solitons in the one-dimensional lattice modeled by the discrete nonlinear Schrodinger equation with the cubic-quintic nonlinearity. Staggered solitons, which were not previously considered in this model, are studied numerically, through the computation of the eigenvalue spectrum for modes of small perturbations, and analytically, by means of the variational approximation. The numerical results confirm the analytical predictions. The mobility of discrete solitons is studied by means of direct simulations, and semianalytically, in the framework of the Peierls-Nabarro barrier, which is introduced in terms of two different concepts, free energy and mapping analysis. It is found that persistently moving localized modes may only be of the unstaggered type.
T2  - Physical Review E
T1  - Staggered and moving localized modes in dynamical lattices with the cubic-quintic nonlinearity
VL  - 77
IS  - 3
DO  - 10.1103/PhysRevE.77.036604
ER  - 

@article{
author = "Maluckov, Aleksandra and Hadžievski, Ljupčo and Malomed, Boris A.",
year = "2008",
abstract = "Results of a comprehensive dynamical analysis are reported for several fundamental species of bright solitons in the one-dimensional lattice modeled by the discrete nonlinear Schrodinger equation with the cubic-quintic nonlinearity. Staggered solitons, which were not previously considered in this model, are studied numerically, through the computation of the eigenvalue spectrum for modes of small perturbations, and analytically, by means of the variational approximation. The numerical results confirm the analytical predictions. The mobility of discrete solitons is studied by means of direct simulations, and semianalytically, in the framework of the Peierls-Nabarro barrier, which is introduced in terms of two different concepts, free energy and mapping analysis. It is found that persistently moving localized modes may only be of the unstaggered type.",
journal = "Physical Review E",
title = "Staggered and moving localized modes in dynamical lattices with the cubic-quintic nonlinearity",
volume = "77",
number = "3",
doi = "10.1103/PhysRevE.77.036604"
}

Maluckov, A., Hadžievski, L.,& Malomed, B. A.. (2008). Staggered and moving localized modes in dynamical lattices with the cubic-quintic nonlinearity. in Physical Review E, 77(3).
https://doi.org/10.1103/PhysRevE.77.036604

Maluckov A, Hadžievski L, Malomed BA. Staggered and moving localized modes in dynamical lattices with the cubic-quintic nonlinearity. in Physical Review E. 2008;77(3).
doi:10.1103/PhysRevE.77.036604 .

Maluckov, Aleksandra, Hadžievski, Ljupčo, Malomed, Boris A., "Staggered and moving localized modes in dynamical lattices with the cubic-quintic nonlinearity" in Physical Review E, 77, no. 3 (2008),
https://doi.org/10.1103/PhysRevE.77.036604 . .