Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1897734 | Physica D: Nonlinear Phenomena | 2008 | 5 Pages |
Abstract
The modulational instability of perturbed plane-wave solutions of the cubic nonlinear Schrödinger (NLS) equation is examined in the presence of three forms of dissipation. We present two families of decreasing-in-magnitude plane-wave solutions to this dissipative NLS equation. We establish that all such solutions that have no spatial dependence are linearly stable, though some perturbations may grow a finite amount. Further, we establish that all such solutions that have spatial dependence are linearly unstable if a certain form of dissipation is present.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
John D. Carter, Cynthia C. Contreras,