Unveiling new insights into soliton solutions and sensitivity analysis of the Shynaray-IIA equation through improved generalized Riccati equation mapping method

The primary aim of this study is to examine the deep characteristics of the Shynaray-IIA equation by applying the improved generalized Riccati equation mapping approach. We derive a dynamical system that is effectively linked to the equation by using the Galilean transformation. Next, we analyze the bifurcation mechanisms in this derived system by applying principles from planar dynamical systems theory. We conducted a thorough investigation of the probable occurrence of chaotic behaviors by introducing a perturbed term into the dynamical system and systematically studying the Shynaray-IIA equation. The inclusion of a thorough two-phase portrayal deepens the scope of this study. We utilized the Runge–Kutta method to thoroughly examine the sensitivity of the dynamical system. The analytical technique allowed us to confirm that slight perturbations in the initial conditions have little impact on the stability of the solution. Furthermore, the advanced technique of utilizing the improved generalized Riccati equation mapping approach is utilized to obtain new exact solutions for the Shynaray-IIA model. We exhibit visual outcomes for individual solutions, providing a comprehensive evaluation by showcasing different results using MATLAB across several dimensions. These solutions and chaotic analysis will be of high significance in all areas of applications of shynaray IIA equation such as optical communications, tsunami and tidal wave phenomena.