Bifurcation and chaotic behaviors to the Sasa–Satsuma and higher-order Sasa–Satsuma equations in fluid dynamics and nonlinear optics

A key objective of the paper is to study the dynamical system for the two types of Sasa–Satsuma equations, namely; Sasa–Satsuma equation and higher-order Sasa–Satsuma equation. A Sasa–Satsuma equation is used to describe the propagation of femtosecond pulses through optical fiber systems. The bifurcation and chaotic characteristic of the Sasa–Satsuma equation and higher-order Sasa–Satsuma equation that arises in fluid dynamics and nonlinear optics are studied. For both models, by using the theory of planar dynamical system the bifurcation and chaotic characteristic of the Sasa–Satsuma equation and higher-order Sasa–Satsuma equation that arises in fluid dynamics and nonlinear optics are studied. For a better understanding of these dynamical behaviors, phase portraits in 2D and 3D figures are dawn. For both equations, the equilibrium points and their effects on the bifurcation behavior are analyzed. Moreover, from the presented results, both models have different dynamical behavior.