Generalized Darboux transformation, semi-rational solutions and novel degenerate soliton solutions for a coupled nonlinear Schrödinger equation

Abstract

In this paper, we obtain two types of semi-rational solutions for a coupled nonlinear Schrodinger equation by applying generalized Darboux transformation (DT). Firstly, we obtain a new DT through a special limit process based on the traditional DT for the equation; then, some nonlinear wave interactions on the zero-intensity background are analyzed under the research of those semi-rational solutions. Based on the above discussion, the dynamics of the interactions between one regular soliton and the type-I degenerate solitons on the zero-intensity background are systematically analyzed by drawing the 3D- and 2D-dimensional plots.