Formation of optical soliton wave profiles of Shynaray-IIA equation via two improved techniques: a comparative study.

This study employs the new extended direct algebraic method and improved sardar sub-equation method to investigate solitary wave solutions in the Shynaray-IIA equation, which characterizes phenomena like tidal waves and tsunamis. These methods transform complex nonlinear coupled partial differential equations into manageable algebraic equations using a traveling wave transformation. Before this study, there is not exiting any research in which someone has obtained such kind of solutions. The main goal is to enhance understanding of the Shynaray-IIA equation behavior in various scenarios. By applying the new extended direct algebraic method and improved sardar sub-equation method, the study derives solitary wave solutions using trigonometric, hyperbolic, and Jacobi functions. By adjusting specific parameters, diverse solutions are obtained, including periodic, bell-shaped, anti-bell-shaped, M-shaped, and W-shaped solitons, each pair exhibiting mathematical symmetry. The analytical soliton solutions are further visualized in both 2D and 3D representations using Mathematica 12.3, aiding in the interpretation of these complex wave phenomena. [ABSTRACT FROM AUTHOR]