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Stability of periodic optical solitons for a nonlinear Schrödinger system

Published online by Cambridge University Press:  21 September 2009

Jaime Angulo Pava  and
Ademir Pastor Ferreira
Jaime Angulo Pava
Affiliation:
Department of Mathematics, IME-USP, Rua do Matão 1010, Cidade Universitária, CEP 05508-090, São Paulo, SP, Brazil (angulo@ime.usp.br)
Ademir Pastor Ferreira
Affiliation:
IMPA, Estrada Dona Castorina 110, CEP 22460-320, Rio de Janeiro, RJ, Brazil (apastor@impa.br)
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Abstract

This paper is concerned with the existence and nonlinear stability of periodic travelling-wave solutions for a nonlinear Schrödinger-type system arising in nonlinear optics. We show the existence of smooth curves of periodic solutions depending on the dnoidal-type functions. We prove stability results by perturbations having the same minimal wavelength, and instability behaviour by perturbations of two or more times the minimal period. We also establish global well posedness for our system by using Bourgain's approach.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 5 , October 2009 , pp. 927 - 959
Copyright
Copyright © Royal Society of Edinburgh 2009

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