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  - 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 . .