Bifurcation, chaotic pattern and optical soliton solutions of generalized nonlinear Schrödinger equation

Abstract

This article studies the generalized nonlinear Schrödinger equation, which is used to simulate the propagation model of optical pulses in Non-Kerr medium. Building upon the traveling wave transformation, the generalized nonlinear Schrödinger equation is simplified to an ordinary differential equation. By employing the two-dimensional planar dynamic system to analyze, the bifurcation, phase portraits and chaotic behaviors of the system is presented. Furthermore, 2D and 3D phase portraits of the dynamic system with perturbation term are plotted with the Maple software. The optical soliton solutions of the generalized nonlinear Schrödinger equation are constructed by using the polynomial complete discriminant method.

Keywords

• Optical soliton solutions
• Planar dynamic system
• Bifurcation
• Non-Kerr medium