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

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.

8 figures

References in corpus (2)

• Spatial Solitons in Optically-Induced Gratings
• Band-gap solitons in nonlinear optically-induced lattices

Cited by in corpus (6)

• Multi-breathers and high order rogue waves for the nonlinear Schrödinger equation on the elliptic function background
• Sine-Gordon Soliton on a Cnoidal Wave Background
• Soliton Solutions of the Toda Hierarchy on Quasi-Periodic Backgrounds Revisited
• The multi elliptic-localized solutions and their asymptotic behaviors for the mKdV equation
• Soliton dynamics in deformable nonlinear lattices
• Negative radiation pressure in Bose-Einstein condensates