Bifurcations and exact traveling wave solutions of Gerdjikov-Ivanov equation with perturbation terms

Abstract

This paper is to find new exact traveling wave solutions of the nonlinear Gerdjikov-Ivanov (for short, GI) equation with perturbation terms. Based on employing the bifurcation theory of planar dynamical systems, we found the exact solutions including periodic wave solution, kink wave solution, anti-kink wave solution and solitary wave solution (bright and dark). Moreover, the explicit expressions of the exact solutions in different parametric domains are given. Finally, we conclude our main results in a theorem at the end of the paper.