Differential and Integral Equations

Nonlinear and spectral stability of periodic traveling wave solutions for a nonlinear Schrödinger system

Ademir Pastor

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Abstract

This paper is concerned with nonlinear and spectral stability of periodic traveling wave solutions for a nonlinear Schrödinger type system arising in nonlinear optics. We prove the existence of two smooth curves of periodic solutions depending on the cnoidal type functions. In the framework established by Grillakis, Shatah and Strauss we prove a stability result under perturbations having the same minimal wavelength and zero mean over their fundamental period. By using the so-called Bloch wave decomposition theory we show spectral stability for a general class of periodic solutions.

Article information

Source
Differential Integral Equations, Volume 23, Number 1/2 (2010), 125-154.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356019391

Mathematical Reviews number (MathSciNet)
MR2588806

Zentralblatt MATH identifier
1228.76031

Subjects
Primary: 76B25: Solitary waves [See also 35C11] 35Q51: Soliton-like equations [See also 37K40] 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]

Citation

Pastor, Ademir. Nonlinear and spectral stability of periodic traveling wave solutions for a nonlinear Schrödinger system. Differential Integral Equations 23 (2010), no. 1/2, 125--154. https://projecteuclid.org/euclid.die/1356019391


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