V. S. Gerdjikov, B. B. Baizakov, M. Salerno, “Modeling Adiabatic $N$-Soliton Interactions and Perturbations”, TMF, 144:2 (2005), 302–312; Theoret. and Math. Phys., 144:2 (2005), 1138

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Teoreticheskaya i Matematicheskaya Fizika, 2005, Volume 144, Number 2, Pages 302–312
DOI: https://doi.org/10.4213/tmf1855 (Mi tmf1855)

This article is cited in 15 scientific papers (total in 15 papers)

Modeling Adiabatic

N

$N$ -Soliton Interactions and Perturbations

V. S. Gerdjikov^a, B. B. Baizakov^bc, M. Salerno^bc

^a Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences
^b University of Salerno
^c INFM — Istituto Nazionale di Fisica della Materia

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DOI: https://doi.org/10.4213/tmf1855

Abstract: We analyze a perturbed version of the complex Toda chain (CTC) in an attempt to describe the adiabatic N-soliton train interactions of the perturbed nonlinear Schrodinger equation. We study perturbations with weak quadratic and periodic external potentials analytically and numerically. The perturbed CTC adequately models the N-soliton train dynamics for both types of potentials. As an application of the developed theory, we consider the dynamics of a train of matter-wave solitons confined in a parabolic trap and an optical lattice.

Keywords: complex Toda chain, adiabatic dynamics, soliton train, expulsion of a soliton.

English version:
Theoretical and Mathematical Physics, 2005, Volume 144, Issue 2, Pages 1138–1146
DOI: https://doi.org/10.1007/s11232-005-0143-5

Bibliographic databases:

Language: Russian

Citation: V. S. Gerdjikov, B. B. Baizakov, M. Salerno, “Modeling Adiabatic

N

$N$ -Soliton Interactions and Perturbations”, TMF, 144:2 (2005), 302–312; Theoret. and Math. Phys., 144:2 (2005), 1138–1146

Citation in format AMSBIB

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https://www.mathnet.ru/eng/tmf1855

https://doi.org/10.4213/tmf1855

https://www.mathnet.ru/eng/tmf/v144/i2/p302

This publication is cited in the following 15 articles:

Vladimir S. Gerdjikov, Michail D. Todorov, “On asymptotic dynamical regimes of Manakov $N$ -soliton trains in adiabatic approximation”, Zhurn. SFU. Ser. Matem. i fiz., 13:6 (2020), 678–693
Gerdjikov V.S., Todorov M.D., Kyuldjiev A.V., “Asymptotic Behavior of Manalcov Solitons: Effects of Potential Wells and Humps”, Math. Comput. Simul., 121 (2016), 166–178
Gerdjikov V.S. Todorov M.D. Kyuldjiev A.V., “Polarization effects in modeling soliton interactions of the Manakov model”, RECENT DEVELOPMENTS IN NONLINEAR ACOUSTICS: 20th International Symposium on Nonlinear Acoustics including the 2nd International Sonic Boom Forum (?cully, France, 29 June?3 July 2015), AIP Conference Proceedings, 1684, ed. Todorov M., Amer Inst Physics, 2015, 080006
M. D. Todorov, A. V. Kyuldjiev, V. S. Gerdjikov, Dynamical Systems and Differential Equations, AIMS Proceedings 2015 Proceedings of the 10th AIMS International Conference (Madrid, Spain), 2015, 505
Todorov M.D. Gerdjikov V.S. Kyuldjiev A.V., “Modeling Interactions of Soliton Trains. Effects of External Potentials”, Application of Mathematics in Technical and Natural Sciences, AIP Conference Proceedings, 1629, ed. Todorov M., Amer Inst Physics, 2014, 186–200
V. S. Gerdjikov, M. D. Todorov, Nonlinear Systems and Complexity, 7, Localized Excitations in Nonlinear Complex Systems, 2014, 147
Gerdjikov V.S. Todorov M.D., “On the Effects of Sech-Like Potentials on Manakov Solitons”, Application of Mathematics in Technical and Natural Sciences, AIP Conference Proceedings, 1561, ed. Todorov M., Amer Inst Physics, 2013, 75–83
Al Khawaja U., “Interaction Forces Among Two-Dimensional Bright Solitons and Many-Soliton Molecules”, Phys. Rev. E, 85:5, Part 2 (2012), 056604
Gerdjikov, VS, “Generalized perturbed complex Toda chain for Manakov system and exact solutions of Bose–Einstein mixtures”, Mathematics and Computers in Simulation, 80:1 (2009), 112
Novoa D, Malomed BA, Michinel H, et al, “Supersolitons: Solitonic excitations in atomic soliton chains”, Physical Review Letters, 101:14 (2008), 144101
Zong, FD, “N-soliton interactions of Bose–Einstein condensates in external potentials”, Acta Physica Sinica, 57:5 (2008), 2658
V.S. Gerdjikov, G. Vilasi, A.B. Yanovski, Lecture Notes in Physics, 748, Integrable Hamiltonian Hierarchies, 2008, 97
Kostov N., Gerdjikov V., “On the soliton interactions in NLS equation with external potentials”, 14th International School on Quantum Electronics: Laser Physics and Applications, Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE), 6604, 2007, S6041–S6041
Gerdjikov VS, Baizakov BB, Salerno M, et al, “Adiabatic N-soliton interactions of Bose–Einstein condensates in external potentials”, Physical Review E, 73:4 (2006), 046606
Barros, VP, “Interaction of solitons in elongated BEC with time-dependent trap”, Journal of Physics B-Atomic Molecular and Optical Physics, 38:22 (2005), 4111

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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