Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1897232 | Physica D: Nonlinear Phenomena | 2008 | 23 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
T. Ivey, S. Lafortune,