Exact solutions of Shynaray-IIA equation (S-IIAE) using the improved modified Sardar sub-equation method

In this paper, we present an innovative approach to acquire the exact solutions of the Shynaray-IIA equations (S-IIAE), by using the improved modified Sardar sub-equation method (IMSSEM). The S-IIAE are nonlinear and coupled partial differential equations that arise in various fields of physics and engineering such as optical fibers and ferromagnetic materials. The IMSSEM is applied to S-IIAE; we successfully derived exact solutions that accurately described the wave propagation behavior of the system under consideration. The obtained solutions include rational, trigonometric, and trigonometric hyperbolic function solutions. The obtained solutions are concise and offer a deeper insight into the dynamics and characteristics of the S-IIAE. Moreover, some of the new solutions to S-IIAE are plotted in different dimensions through which bright, anti-kink and bright solitary wave structures are established. The results of the study also indicated that the proposed method is a valuable approach for achieving analytical solutions to a wide range of nonlinear partial differential equations.