Formation of optical solitons for the nonlinear generalized (3+1)-dimensional Sasa–Satsuma equation

In this study, accurate solitary wave solutions of the generalized (3+1)-dimensional Sasa–Satsuma equation are investigated using the modified F-expansion approach and the extended hyperbolic function method. The model under consideration describes the propagation of ultrashort optical pulses in nonlinear optical fibers, where nonlinear derivative terms, self-steepening and third-order dispersion are important higher-order effects. A wide range of analytical solutions, including solitonic, trigonometric, rational and exponential wave shapes, are derived using the modified F-expansion method. Additionally, the extended hyperbolic function method is used to generate bright, dark and singular soliton solutions as well as periodic wave solutions under appropriate parametric restrictions. Furthermore, modulation instability is examined using linear stability theory, and the parameter regimes in which the solutions become unstable are determined using the associated dispersion relation. The acquired solutions are unique and have not been documented in the current literature, as far as we are aware. The suggested techniques are useful tools for the analysis of a broad class of nonlinear evolution equations because they are simple, effective and widely applicable. Graphical representations are used to help clarify the physical properties of the generated solutions.