Science and Mathematics Faculty Publications

Title

On the Construction of Orbits Homoclinic to Plane Waves in Integrable Coupled Nonlinear Schroedinger Systems

Document Type

Article

Publication Date

2-14-2000

Journal Title

Physics Letters A

Volume

266

Issue

1

First Page

24

Last Page

33

Abstract

Plane waves of coupled NLS PDEs are known to possess self-focusing and cross-coupling instabilities. In the integrable limit of coupled NLS systems, these instabilities are accompanied by homoclinic orbits which asymptotically (in time) approach the unstable plane wave. Here we use the integrable method of Backlund transformations to construct a two-parameter family of exact spatially periodic CNLS solutions, which consist of a plane wave connected to a nonlinear superposition of self-focusing and cross-coupling homoclinic orbits.

Keywords

[pacs] 02.30.Jr, [pacs] 42.65.Sf, Backlund transformation, Gauge transformation, Lax pair, Homoclinic orbit, Coupling instability

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