Science and Mathematics Faculty Publications

Title

Homoclinic Connections of Unstable Plane Waves of the Long-wave-short-wave Equations

Document Type

Article

Publication Date

7-2006

Journal Title

Studies in Applied Mathematics

Volume

117

Issue

1

First Page

71

Last Page

93

Abstract

A Bäcklund transformation is obtained for unstable plane wave solutions of the long-wave–short-wave resonance equations that appear in continuum mechanics. Explicit expressions for the periodic homoclinic connections that arise from the instabilities are constructed by evaluating the transform at double points of the Floquet spectral curve.

Keywords

Wave equation, Bäcklund transformation, differential equations, configuration space, continuum mechanics, Floquet theory

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