Spectral stability of periodic NLS and CGL solutions

Details Spectral stability of periodic NLS and CGL solutions Spectral stability of periodic NLS and CGL solutions

2007-05-08

arxiv.org/abs/0705.1164v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

26 pages, 12 figures

Scientific paper

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.

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