Spectral stability analysis for periodic traveling wave solutions of NLS and CGL perturbations
نویسندگان
چکیده
We consider cnoidal traveling wave solutions to the focusing nonlinear Schrödinger equation (NLS) that have been shown to persist when the NLS is perturbed to the complex Ginzburg–Landau equation (CGL). We show that while these periodic traveling waves are spectrally stable solutions of NLS with respect to periodic perturbations, they are unstable with respect to bounded perturbations. Furthermore, we use an argument based on the Fredholm alternative to find an instability criterion for the persisting solutions to CGL. c © 2008 Elsevier B.V. All rights reserved.
منابع مشابه
Spectral stability of periodic NLS and CGL solutions
We consider periodic traveling wave solutions to the focusing nonlinear Schrödinger 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 a...
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