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

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

2003-12-22

arxiv.org/abs/nlin/0312052v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

8 figures

Scientific paper

10.1088/0305-4470/37/33/004

An application of the Darboux transformation on a cnoidal wave background in the coupled nonlinear Schr\"{o}dinger 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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