Solitary, periodic, kink wave solutions of a perturbed high-order nonlinear Schrödinger equation via bifurcation theory

Abstract

In this paper, by using the bifurcation theory for dynamical system, we construct traveling wave solutions of a high-order nonlinear Schrödinger equation with a quintic nonlinearity. Firstly, based on wave variables, the equation is transformed into an ordinary differential equation. Then, under the parameter conditions, we obtain the Hamiltonian system and phase portraits. Finally, traveling wave solutions which contains solitary, periodic and kink wave solutions are constructed by integrating along the homoclinic or heteroclinic orbits. In addition, by choosing appropriate values to parameters, different types of structures of solutions can be displayed graphically. Moreover, the computational work and it's figures show that this technique is influential and efficient.

Keywords

• Traveling wave solution
• High-order nonlinear Schrödinger equation
• Bifurcation theory
• Dynamical system
• Hamiltonian system