The Dynamical Behavior Analysis and the Traveling Wave Solutions of the Stochastic Sasa–Satsuma Equation

In this article, the phase portraits, chaotic patterns, and traveling wave solutions of the stochastic Sasa–Satsuma equation are investigated. Firstly, the stochastic Sasa–Satsuma equation is transformed into an ordinary differential equation through traveling wave transformation. Secondly, two-dimensional planar dynamical system is presented by using the theory of planar dynamical systems. Then, the three-dimensional and two-dimensional phase portraits of the dynamical system are drawn by using Maple software. Finally, the complete discriminant system method is used to solve the stochastic Sasa-Satsuma equation, resulting in many solutions that other methods cannot obtain, including rational, trigonometric, hyperbolic, and Jacobi elliptic function solutions. Moreover, three-dimensional-surface plots and two-dimensional-shape plots for the module length of some solutions under different parameters are drawn by using Maple software. The innovation of this article lies in introducing stochastic parameters into the Sasa–Satsuma equation, obtaining more diverse and comprehensive conclusions.