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

PHYSICA D-NONLINEAR PHENOMENA

卷:237

Article

Carter, John D.¹  Contreras, Cynthia C.² 

[1] Seattle Univ, Dept Math, Seattle, WA 98122 USA

[2] Corning Inc, Display Technol, Corning, NY 14831 USA

关键词: NLS;    Nonlinear Schrodinger equation;    Dissipative;    Complex Ginzburg-Landau equation;    Plane waves;    Stability;   

DOI  :  10.1016/j.physd.2008.07.016

来源: Elsevier

【 摘 要 】

The modulational instability of perturbed plane-wave solutions of the cubic nonlinear Schrodinger (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. we establish that all such solutions that have spatial dependence are linearly unstable if a certain Further, form of dissipation is present. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

Free