Plane-wave solutions of a dissipative generalization of the vector nonlinear Schrödinger equation

John D. Carter

Mathematics and Computers in Simulation (MATCOM), 2012, vol. 82, issue 6, 1038-1046

Abstract: The modulational instability of perturbed plane-wave solutions of the vector nonlinear Schrödinger (VNLS) equation is examined in the presence of multiple forms of dissipation. We establish that all constant-magnitude solutions of the dissipative VNLS equation are less unstable than their counterparts in the conservative VNLS equation. We also present three families of decreasing-in-magnitude plane-wave solutions to this dissipative VNLS equation. We establish that if certain forms of dissipation are present, then all exponentially-decaying plane-wave solutions with spatial dependence are linearly unstable while those without spatial dependence are linearly stable.

Keywords: Nonlinear; NLS; Stability; Plane-waves; Dissipation (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:82:y:2012:i:6:p:1038-1046

DOI: 10.1016/j.matcom.2010.07.032

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