Malomed, Boris A.

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979cd497-d6cb-4e7b-8999-e41704e6c4f9
  • Malomed, Boris A. (15)
  • Malomed, Boris A (1)
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Author's Bibliography

Modulational Instability, Inter-Component Asymmetry, and Formation of Quantum Droplets in One-Dimensional Binary Bose Gases

Mithun, Thudiyangal; Maluckov, Aleksandra; Kasamatsu, Kenichi; Malomed, Boris A; Khare, Avinash

(2020)

TY  - JOUR
AU  - Mithun, Thudiyangal
AU  - Maluckov, Aleksandra
AU  - Kasamatsu, Kenichi
AU  - Malomed, Boris A
AU  - Khare, Avinash
PY  - 2020
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8977
AB  - Quantum droplets are ultradilute liquid states that emerge from the competitive interplay of two Hamiltonian terms, the mean-field energy and beyond-mean-field correction, in a weakly interacting binary Bose gas. We relate the formation of droplets in symmetric and asymmetric two-component one-dimensional boson systems to the modulational instability of a spatially uniform state driven by the beyond-mean-field term. Asymmetry between the components may be caused by their unequal populations or unequal intra-component interaction strengths. Stability of both symmetric and asymmetric droplets is investigated. Robustness of the symmetric solutions against symmetry-breaking perturbations is confirmed.
T2  - Symmetry
T1  - Modulational Instability, Inter-Component Asymmetry, and Formation of Quantum Droplets in One-Dimensional Binary Bose Gases
VL  - 12
IS  - 1
SP  - 174
DO  - 10.3390/sym12010174
ER  - 
@article{
author = "Mithun, Thudiyangal and Maluckov, Aleksandra and Kasamatsu, Kenichi and Malomed, Boris A and Khare, Avinash",
year = "2020",
abstract = "Quantum droplets are ultradilute liquid states that emerge from the competitive interplay of two Hamiltonian terms, the mean-field energy and beyond-mean-field correction, in a weakly interacting binary Bose gas. We relate the formation of droplets in symmetric and asymmetric two-component one-dimensional boson systems to the modulational instability of a spatially uniform state driven by the beyond-mean-field term. Asymmetry between the components may be caused by their unequal populations or unequal intra-component interaction strengths. Stability of both symmetric and asymmetric droplets is investigated. Robustness of the symmetric solutions against symmetry-breaking perturbations is confirmed.",
journal = "Symmetry",
title = "Modulational Instability, Inter-Component Asymmetry, and Formation of Quantum Droplets in One-Dimensional Binary Bose Gases",
volume = "12",
number = "1",
pages = "174",
doi = "10.3390/sym12010174"
}
Mithun, T., Maluckov, A., Kasamatsu, K., Malomed, B. A.,& Khare, A.. (2020). Modulational Instability, Inter-Component Asymmetry, and Formation of Quantum Droplets in One-Dimensional Binary Bose Gases. in Symmetry, 12(1), 174.
https://doi.org/10.3390/sym12010174
Mithun T, Maluckov A, Kasamatsu K, Malomed BA, Khare A. Modulational Instability, Inter-Component Asymmetry, and Formation of Quantum Droplets in One-Dimensional Binary Bose Gases. in Symmetry. 2020;12(1):174.
doi:10.3390/sym12010174 .
Mithun, Thudiyangal, Maluckov, Aleksandra, Kasamatsu, Kenichi, Malomed, Boris A, Khare, Avinash, "Modulational Instability, Inter-Component Asymmetry, and Formation of Quantum Droplets in One-Dimensional Binary Bose Gases" in Symmetry, 12, no. 1 (2020):174,
https://doi.org/10.3390/sym12010174 . .
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16

Nonlinear localized flat-band modes with spin-orbit coupling

Gligorić, Goran; Maluckov, Aleksandra; Hadžievski, Ljupčo; Flach, Sergej; Malomed, Boris A.

(2016)

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 . .
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Nonlinear localized flat-band modes with spin-orbit coupling

Gligorić, Goran; Maluckov, Aleksandra; Hadžievski, Ljupčo; Flach, Sergej; Malomed, Boris A.

(2016)

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 . .
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Composite localized modes in discretized spin-orbit-coupled Bose-Einstein condensates

Beličev, Petra; Gligorić, Goran; Petrović, Jovana S.; Maluckov, Aleksandra; Hadžievski, Ljupčo; Malomed, Boris A.

(2015)

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 . .
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Localized modes in mini-gaps opened by periodically modulated intersite coupling in two-dimensional nonlinear lattices

Gligorić, Goran; Maluckov, Aleksandra; Hadžievski, Ljupčo; Malomed, Boris A.

(2014)

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. (C) 2014 AIP Publishing LLC.
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. (C) 2014 AIP Publishing LLC.",
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 . .
1
4
4
4

Discrete solitons in an array of quantum dots

Gligorić, Goran; Maluckov, Aleksandra; Hadžievski, Ljupčo; Slepyan, Gregory Ya.; Malomed, Boris A.

(2013)

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 . .
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14
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14

High- and low-frequency phonon modes in dipolar quantum gases trapped in deep lattices

Maluckov, Aleksandra; Gligorić, Goran; Hadžievski, Ljupčo; Malomed, Boris A.; Pfau, Tilman

(2013)

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 . .
1
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8

Discrete localized modes supported by an inhomogeneous defocusing nonlinearity

Gligorić, Goran; Maluckov, Aleksandra; Hadžievski, Ljupčo; Malomed, Boris A.

(2013)

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 . .
1
8
8
8

Stable Periodic Density Waves in Dipolar Bose-Einstein Condensates Trapped in Optical Lattices

Maluckov, Aleksandra; Gligorić, Goran; Hadžievski, Ljupčo; Malomed, Boris A.; Pfau, Tilman

(2012)

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 . .
1
28
28

Transition to miscibility in linearly coupled binary dipolar Bose-Einstein condensates

Gligorić, Goran; Maluckov, Aleksandra; Stepić, Milutin; Hadžievski, Ljupčo; Malomed, Boris A.

(2010)

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 . .
26
26

Two-dimensional discrete solitons in dipolar Bose-Einstein condensates

Gligorić, Goran; Maluckov, Aleksandra; Stepić, Milutin; Hadžievski, Ljupčo; Malomed, Boris A.

(2010)

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 . .
41
40
40

Soliton stability and collapse in the discrete nonpolynomial Schrodinger equation with dipole-dipole interactions

Gligorić, Goran; Maluckov, Aleksandra; Hadžievski, Ljupčo; Malomed, Boris A.

(2009)

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 . .
36
34

Bright solitons in the one-dimensional discrete Gross-Pitaevskii equation with dipole-dipole interactions

Gligorić, Goran; Maluckov, Aleksandra; Hadžievski, Ljupčo; Malomed, Boris A.

(2008)

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 . .
55
52

Solitons in the discrete nonpolynomial Schrodinger equation

Maluckov, Aleksandra; Hadžievski, Ljupčo; Malomed, Boris A.; Salasnich, Luca

(2008)

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 . .
30
31

Staggered and moving localized modes in dynamical lattices with the cubic-quintic nonlinearity

Maluckov, Aleksandra; Hadžievski, Ljupčo; Malomed, Boris A.

(2008)

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 . .
17
17

Dark solitons in dynamical lattices with the cubic-quintic nonlinearity

Maluckov, Aleksandra; Hadžievski, Ljupčo; Malomed, Boris A.

(2007)

TY  - JOUR
AU  - Maluckov, Aleksandra
AU  - Hadžievski, Ljupčo
AU  - Malomed, Boris A.
PY  - 2007
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/3312
AB  - Results of systematic studies of discrete dark solitons (DDSs) in the one-dimensional discrete nonlinear Schrodinger equation with the cubic-quintic on-site nonlinearity are reported. The model may be realized as an array of optical waveguides made of an appropriate non-Kerr material. First, regions free of the modulational instability are found for staggered and unstaggered cw states, which are then used as the background supporting DDS. Static solitons of both on-site and inter-site types are constructed. Eigenvalue spectra which determine the stability of DDSs against small perturbations are computed in a numerical form. For on-site solitons with the unstaggered background, the stability is also examined by dint of an analytical approximation, that represents the dark soliton by a single lattice site at which the field is different from cw states of two opposite signs that form the background of the DDS. Stability regions are identified for the DDSs of three types: unstaggered on-site, staggered on-site, and staggered inter-site; all unstaggered inter-site dark solitons are unstable. A remarkable feature of the model is coexistence of stable DDSs of the unstaggered and staggered types. The predicted stability is verified in direct simulations; it is found that unstable unstaggered DDSs decay, while unstable staggered ones tend to transform themselves into moving dark breathers. A possibility of setting DDS in motion is studied too. Analyzing the respective Peierls-Nabarro potential barrier, and using direct simulations, we infer that unstaggered DDSs cannot move, but their staggered counterparts can be readily set in motion.
T2  - Physical Review E
T1  - Dark solitons in dynamical lattices with the cubic-quintic nonlinearity
VL  - 76
IS  - 4
DO  - 10.1103/PhysRevE.76.046605
ER  - 
@article{
author = "Maluckov, Aleksandra and Hadžievski, Ljupčo and Malomed, Boris A.",
year = "2007",
abstract = "Results of systematic studies of discrete dark solitons (DDSs) in the one-dimensional discrete nonlinear Schrodinger equation with the cubic-quintic on-site nonlinearity are reported. The model may be realized as an array of optical waveguides made of an appropriate non-Kerr material. First, regions free of the modulational instability are found for staggered and unstaggered cw states, which are then used as the background supporting DDS. Static solitons of both on-site and inter-site types are constructed. Eigenvalue spectra which determine the stability of DDSs against small perturbations are computed in a numerical form. For on-site solitons with the unstaggered background, the stability is also examined by dint of an analytical approximation, that represents the dark soliton by a single lattice site at which the field is different from cw states of two opposite signs that form the background of the DDS. Stability regions are identified for the DDSs of three types: unstaggered on-site, staggered on-site, and staggered inter-site; all unstaggered inter-site dark solitons are unstable. A remarkable feature of the model is coexistence of stable DDSs of the unstaggered and staggered types. The predicted stability is verified in direct simulations; it is found that unstable unstaggered DDSs decay, while unstable staggered ones tend to transform themselves into moving dark breathers. A possibility of setting DDS in motion is studied too. Analyzing the respective Peierls-Nabarro potential barrier, and using direct simulations, we infer that unstaggered DDSs cannot move, but their staggered counterparts can be readily set in motion.",
journal = "Physical Review E",
title = "Dark solitons in dynamical lattices with the cubic-quintic nonlinearity",
volume = "76",
number = "4",
doi = "10.1103/PhysRevE.76.046605"
}
Maluckov, A., Hadžievski, L.,& Malomed, B. A.. (2007). Dark solitons in dynamical lattices with the cubic-quintic nonlinearity. in Physical Review E, 76(4).
https://doi.org/10.1103/PhysRevE.76.046605
Maluckov A, Hadžievski L, Malomed BA. Dark solitons in dynamical lattices with the cubic-quintic nonlinearity. in Physical Review E. 2007;76(4).
doi:10.1103/PhysRevE.76.046605 .
Maluckov, Aleksandra, Hadžievski, Ljupčo, Malomed, Boris A., "Dark solitons in dynamical lattices with the cubic-quintic nonlinearity" in Physical Review E, 76, no. 4 (2007),
https://doi.org/10.1103/PhysRevE.76.046605 . .
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