Chaotic pattern, bifurcation, sensitivity and traveling wave solution of the coupled Kundu–Mukherjee–Naskar equation

Abstract

In this paper, the coupled Kundu–Mukherjee–Naskar equation is considered, which is usually used to describe the oceanic rogue waves, hole waves and Bragg grating fibers. Firstly, the traveling wave transformation is applied to convert the coupled Kundu–Mukherjee–Naskar equation into two-dimensional planar dynamic system. Secondly, bifurcation and two-dimensional phase portrait of the coupled Kundu–Mukherjee–Naskar equation are discussed by using the plane dynamics system. What is more, after adding periodic perturbation term, two-dimensional phase portrait, three-dimensional phase portrait, Poincaré section and sensitivity of its perturbed system are plotted by the Maple software. Finally, the optical soliton solutions of the coupled Kundu–Mukherjee–Naskar equation are obtained by using planar dynamical system method.