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

Jaroslaw E. Prilepsky*, Stanislav A. Derevyanko

*Corresponding author for this work

Research output: Contribution to journalArticle

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.

Original languageEnglish
Article number036616
Number of pages9
JournalPhysical Review E
Volume75
Issue number3
DOIs
Publication statusPublished - 28 Mar 2007

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Breakup
Damped
nonlinear equations
Nonlinear Equations
Linearly
Perturbation Theory
Solitons
eigenvalues
perturbation theory
solitary waves
Eigenvalue
Spectral Problem
Small Perturbations
Bound States
Demonstrate
Numerical Solution
occurrences
perturbation

Bibliographical note

©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

Cite this

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title = "Breakup of a multisoliton state of the linearly damped nonlinear Schr{\"o}dinger equation",
abstract = "We address the breakup (splitting) of multisoliton solutions of the nonlinear Schr{\"o}dinger 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.",
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Breakup of a multisoliton state of the linearly damped nonlinear Schrödinger equation. / Prilepsky, Jaroslaw E.; Derevyanko, Stanislav A.

In: Physical Review E, Vol. 75, No. 3, 036616, 28.03.2007.

Research output: Contribution to journalArticle

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