Vector combined cnoidal wave and soliton solutions for a 3D partially nonlocal CNLSE

Abstract

A 3D distributed-coefficient coupled nonlinear Schrödinger equation(CNLSE) with the partially nonlocal nonlinearity(PNN) for locality in two transverse directions and non-locality in the longitudinal direction becomes the center of attention in this paper. A one-to-one corresponding expression from the distributed-coefficient CNLSE with the PNN to the constant-coefficient CNLSE is confirmed. By way of the Darboux transformation, combined vector solutions of cnoidal wave and soliton with different structures for double components are found. Evolutional behaviors of dark-bright soliton pair, dark-bright soliton pair traveling parallelly along the top of cnoidal wave, and soliton break-up are revealed when parameters of solutions are selected as different values.

Keywords

• Vector combined solutions of cnoidal wave and soliton
• Coupled nonlinear Schrödinger equation
• Partially nonlocal nonlinearity