Breakup of a multisoliton state of the linearly damped nonlinear Schrödinger equation

Prilepsky, Jaroslaw E. and Derevyanko, Stanislav A. (2007). Breakup of a multisoliton state of the linearly damped nonlinear Schrödinger equation. Physical Review E, 75 (3),

Abstract

We address the breakup (splitting) of multisoliton solutions of the nonlinear Schrödinger equation (NLSE), occurring due to linear loss. Two different approaches are used for the study of the splitting process. The first one is based on the direct numerical solution of the linearly damped NLSE and the subsequent analysis of the eigenvalue drift for the associated Zakharov-Shabat spectral problem. The second one involves the multisoliton adiabatic perturbation theory applied for studying the evolution of the solution parameters, with the linear loss taken as a small perturbation. We demonstrate that in the case of strong nonadiabatic loss the evolution of the Zakharov-Shabat eigenvalues can be quite nontrivial. We also demonstrate that the multisoliton breakup can be correctly described within the framework of the adiabatic perturbation theory and can take place even due to small linear loss. Eventually we elucidate the occurrence of the splitting and its dependence on the phase mismatch between the solitons forming a two-soliton bound state.

Publication DOI: https://doi.org/10.1103/PhysRevE.75.036616
Divisions: Engineering & Applied Sciences > Mathematics
Engineering & Applied Sciences > Systems analytics research institute (SARI)
Engineering & Applied Sciences > Electrical, Electronic & Power Engineering
Additional Information: ©2007 The American Physical Society. Breakup of a multisoliton state of the linearly damped nonlinear Schrödinger equation Jaroslaw E. Prilepsky and Stanislav A. Derevyanko Phys. Rev. E 75, 036616 – Published 28 March 2007
Uncontrolled Keywords: Physics and Astronomy(all),Condensed Matter Physics,Statistical and Nonlinear Physics,Mathematical Physics
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Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
http://journals ... sRevE.75.036616 (Publisher URL)
Published Date: 2007-03-28
Authors: Prilepsky, Jaroslaw E. ( 0000-0002-3035-4112)
Derevyanko, Stanislav A.

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