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Kvantovaya Elektronika, 2005, Volume 35, Number 10, Pages 929–937 (Mi qe3442)  

This article is cited in 54 scientific papers (total in 54 papers)

Solitons

Dynamics of solitons in the model of nonlinear Schrödinger equation with an external harmonic potential: II. Dark Solitons

C. Hernandez Tenorio, E. Villagran Vargas, V. N. Serkin, M. Agüero Granados, T. L. Belyaeva, R. Peña Moreno, L. Morales Lara

Benemérita Universidad Autónoma de Puebla, Mexico
Abstract: The dynamics of dark solitons is studied within the framework of the mathematical model of nonlinear Schrödinger equation (NSE) with an external harmonic potential. A comparative analysis of the solutions of nonstationary problems is performed for a linear harmonic oscillator and the NSE model with a harmonic potential for different signs of the self-action potential. It is shown that the main specific feature of the dynamics of dark NSE solitons in a parabolic trap is the formation of solitons with dynamically changing form factors producing the periodic variation in the modulation depth (the degree of 'blackness') of dark solitons. The oscillation period of the dark soliton does not coincide with the oscillation period of a linear quantum-mechanical oscillator, which is caused by the periodic transformation of the black soliton to the grey one and vice versa. The conditions of applicability of the method of inverse scattering problem are presented, the generalised Lax pair is found, and exact soliton solutions are given for the mathematical NSE model with an external harmonic potential.
Received: 19.11.2004
Revised: 14.07.2005
English version:
Quantum Electronics, 2005, Volume 35, Issue 10, Pages 929–937
DOI: https://doi.org/10.1070/QE2005v035n10ABEH003442
Bibliographic databases:
Document Type: Article
PACS: 03.75.Fi, 05.45.Yv, 42.65.Tg
Language: Russian


Citation: C. Hernandez Tenorio, E. Villagran Vargas, V. N. Serkin, M. Agüero Granados, T. L. Belyaeva, R. Peña Moreno, L. Morales Lara, “Dynamics of solitons in the model of nonlinear Schrödinger equation with an external harmonic potential: II. Dark Solitons”, Kvantovaya Elektronika, 35:10 (2005), 929–937 [Quantum Electron., 35:10 (2005), 929–937]
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