Phase portraits and optical soliton solutions of coupled Sasa–Satsuma model in birefringent fibers

Abstract

The main purpose of this paper is to discuss the optical soliton solutions and phase portraits of the coupled Sasa–Satsuma model in nonlinear optics. This model is usually used to describe the propagation of femtosecond pulses in optical fibers. By using traveling wave transformation, the coupled Sasa–Satsuma model is simplified into the coupled nonlinear ordinary differential equations. After that, the coupled nonlinear ordinary differential equations are transformed into two-dimensional planar dynamic system with the Hamiltonian system. According to the bifurcation theory of planar dynamical system, the phase portrait of two-dimensional dynamical system is drawn. What is more, some very important optical soliton solutions are also constructed. In order to explain the propagation of optical solitons, three-dimensional diagrams, two-dimensional diagrams and the contour plots of the obtained solutions are drawn by using Maple software.

Keywords

• Coupled Sasa–Satsuma equation
• Phase portrait
• Optical soliton solution
• Planar dynamic system method