Exploring solitary wave solutions of extended Sakovich equations: A focus on nonlinear science

This aim of this work is to apply three proposed mathematical methods, namely, enhanced simple equation, [Formula: see text]-expansion and modified F-expansion to investigate solitary wave solutions for the two recently developed extended Sakovich equations in the context of [Formula: see text]- and [Formula: see text]-dimensional structures. The equations under this study belong to the category of Korteweg–de Vries (KdV) equations which are widely acknowledged as important components of fluid dynamics. Many scientific fields, including mathematics, physics, soliton theory, plasma physics, biology, chemistry, and nonlinear processes can benefit from the use of these equations. The derived solutions are in the form of Trigonometric, hyperbolic, exponential and rational functions. The Mathematica 13 computational software is used to represent some solutions graphically in two- and three-dimensional for the physical phenomena of concern models. Therefore, our work’s inventiveness is demonstrated by the application of many types of new solutions and newly employed creative ways. This facilitates additional research into nonlinear models that realistically capture important physical processes in daily life.