Bifurcations and New Exact Travelling Wave Solutions of the Coupled Nonlinear Schrödinger-KdV Equations

Abstract

By using the method of dynamical system, the exact travelling wave solutions of the coupled nonlinear Schrödinger-KdV equations are studied. Based on this method, all phase portraits of the system in the parametric space are given. All possible bounded travelling wave solutions such as solitary wave solutions and periodic travelling wave solutions are obtained. With the aid of Maple software, the numerical simulations are conducted for solitary wave solutions and periodic travelling wave solutions to the coupled nonlinear Schrödinger-KdV equations. The results show that the presented findings improve the related previous conclusions.