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Fast-moving finite and infinite trains of solitons for nonlinear Schrödinger equations

Part of: Equations of mathematical physics and other areas of application Representations of solutions

Published online by Cambridge University Press:  23 November 2015

Stefan Le Coz ,
Dong Li  and
Tai-Peng Tsai
Stefan Le Coz
Affiliation:
Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 9, France (slecoz@math.univ-toulouse.fr)
Dong Li
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada and Institute for Advanced Study, 1st Einstein Drive, Princeton, NJ 08544, USA (mpdongli@gmail.com)
Tai-Peng Tsai
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada (ttsai@math.ubc.ca)
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Abstract

We study infinite soliton trains solutions of nonlinear Schrödinger equations, i.e. solutions behaving as the sum of infinitely many solitary waves at large time. Assuming the composing solitons have sufficiently large relative speeds, we prove the existence and uniqueness of such a soliton train. We also give a new construction of multi-solitons (i.e. finite trains) and prove uniqueness in an exponentially small neighbourhood, and we consider the case of solutions composed of several solitons and kinks (i.e. solutions with a non-zero background at infinity).

Keywords

soliton trainmulti-soliton solutionmulti-kink solutionnonlinear Schrödinger equation

MSC classification

Secondary: 35Q55: NLS-like equations (nonlinear Schrödinger) 35C08: Soliton solutions 35Q51: Soliton-like equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 145 , Issue 6 , December 2015 , pp. 1251 - 1282
Copyright
Copyright © Royal Society of Edinburgh 2015 

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