Bifurcations, chaotic behavior, sensitivity analysis and new optical solitons solutions of Sasa-Satsuma equation

The Sasa-Satsuma (SS) equation is studied in this research study using ideas from planar dynamical theory and the beta differential operator. The SS equation is converted into two ordinary differential equations by applying the Galilean transformation. The work is since concentrated on examining the system's bifurcation points and equilibrium points. The sensitivity of the linked system to its initial values is demonstrated via graphical representations. In order to examine chaos and phase transitions, the system is changed by adding the periodic function cos(omega t)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\cos (\omega t)$$\end{document}. This modification is done as part of this study. Specific optical soliton solutions are illustrated using the first integral technique. Additionally, for various combinations of frequency and amplitude values, numerical simulations are demonstrated the existence of unusual chaotic attractors, such as candy-type, torus-type, and multiscroll chaotic structures. The impact of the beta differential operator on the amplitude of various optical solitons, such as bright, dark, W-shaped, and breather solitons, are also studied.