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arXiv · nlin/0312052

Soliton on a Cnoidal Wave Background in the coupled nonlinear Schrödinger equation

H. J. Shin
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Abstract

An application of the Darboux transformation on a cnoidal wave background in the coupled nonlinear Schrödinger equation gives a new solution which describes a soliton moving on a cnoidal wave. This is a generalized version of the previously known soliton solutions of dark-bright pair. Here a dark soliton resides on a cnoidal wave instead of on a constant background. It also exhibits a new types of soliton solution in a self-focusing medium, which describes a breakup of a generalized dark-bright pair into another generalized dark-bright pair and an "oscillating" soliton. We calculate the shift of the crest of the cnoidal wave along a soliton and the moving direction of the soliton on a cnoidal wave.

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H. J. Shin. 2003-12-22. Soliton on a Cnoidal Wave Background in the coupled nonlinear Schrödinger equation. https://doi.org/10.1088/0305-4470%2F37%2F33%2F004

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