Stability of plane-wave solutions of a dissipative generalization of the nonlinear Schrödinger equation

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...

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Bibliographic Details
Published in:Physica. D 2008-12, Vol.237 (24), p.3292-3296
Main Authors: Carter, John D., Contreras, Cynthia C.
Format: Article
Language:English
Subjects:
Complex Ginzburg–Landau equation
Dissipative
Exact sciences and technology
NLS
Nonlinear Schrödinger equation
Physics
Plane waves
Stability
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Summary: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.
ISSN:0167-2789
1872-8022
DOI:10.1016/j.physd.2008.07.016