Bifurcation Analysis and Solutions of a Higher-Order Nonlinear Schrödinger Equation

Abstract EN

The purpose of this paper is to investigate a higher-order nonlinear Schrödinger equation with non-Kerr term by using the bifurcation theory method of dynamical systems and to provide its bounded traveling wave solutions.

Applying the theory, we discuss the bifurcation of phase portraits and investigate the relation between the bounded orbit of the traveling wave system and the energy level.

Through the research, new traveling wave solutions are given, which include solitary wave solutions, kink wave solutions, and periodic wave solutions.