Stability of plane-wave solutions of a dissipative generalization of the nonlinear Schrödinger equation |
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Authors: | John D. Carter Cynthia C. Contreras |
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Affiliation: | a Mathematics Department, Seattle University, 901 12th Avenue, Seattle, WA 98122, United States b Display Technologies, Corning, Incorporated, Corning, NY 14831, United States |
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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. |
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Keywords: | NLS Nonlinear Schrö dinger equation Dissipative Complex Ginzburg-Landau equation Plane waves Stability |
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