Propagation of optical solitons and dispersive solitary wave structure in complex media to the nonlinear integrable system via computational technique.

The nonlinear complex Shynaray-IIA (S-IIA) system is investigated in the present study. The main objective of this research to explore optical soliton solutions of the nonlinear complex Shynaray-IIA system using the auxiliary equation method. The obtained solutions exhibit novel and diverse physical structures, including periodic waves, peakon dark, bell bright, kink waves, peakon bright, anti-kink waves, bell dark, breather solitons, mixed bright and dark, mixed kink bright and dark, and mixed anti-kink bright and dark wave solitons. Furthermore, using Mathematica software, three-dimensional, two-dimensional, and contour plots have been generated to illustrate the physical behavior of the derived solutions by assigning appropriate constant parameters through symbolic computation. The obtained solutions are original, novel, and have not been previously examined for the Shynaray-IIA system. These results are expected to be useful for studying nonlinear phenomena in physical sciences and engineering. The proposed method is significant for addressing new problems and applying previously untested approaches, leading to the derivation of several exact and optical soliton solutions. The results demonstrate the simplicity, power, and efficiency of this technique for analyzing a variety of nonlinear problems in both real and complex forms.