Spectral stability of periodic NLS and CGL solutions
Exactly Solvable and Integrable Systems
2007-05-23 v1
Abstract
We consider periodic traveling wave solutions to the focusing nonlinear Schrodinger equation (NLS) that have been shown to persist when the NLS is perturbed to the complex Ginzburg-Landau equation (CGL). In particular, we show that these periodic traveling waves are spectrally stable solutions of NLS with respect to periodic perturbations. Furthermore, we use an argument based on the Fredholm alternative to find an instability criterion for the persisting solutions to CGL.
Keywords
Cite
@article{arxiv.0705.1164,
title = {Spectral stability of periodic NLS and CGL solutions},
author = {Thomas Ivey and Stephane Lafortune},
journal= {arXiv preprint arXiv:0705.1164},
year = {2007}
}
Comments
26 pages, 12 figures