<p>This study presents a novel investigation of soliton and solitary wave solutions to the nonlinear Shynaray-IIA (S-IIA) equation using the extended simple equation method, an efficient analytical approach. The nonlinear Shynaray-IIA equation has significant applications in various fields of engineering and physics, including ferromagnetism, nonlinear optics, and fiber optics. In this work, several new soliton structures are derived that accurately describe wave propagation behavior through symbolic computation. The exact solutions are expressed in terms of hyperbolic, exponential, and trigonometric functions. These results are concise, interesting, and provide deeper insights into the dynamical characteristics of the model. A graphical analysis of selected solutions is carried out using real, imaginary, and absolute functions, visualized through three-dimensional, two-dimensional, and contour plots generated by numerical simulation. The physical structures obtained with diverse structure of solitons include periodic, peakon, bell-shaped, bright, anti-kink waves, dark, kink waves, and solitary wave solutions. Furthermore, the proposed technique can be effectively applied to other nonlinear problems to derive analytical solutions.</p>