Analytical Exploration of the (4+1)-Dimensional Fokas Equation: Exact Traveling Wave Solutions

Abstract

This research paper aims at obtaining closed-form solutions for the traveling wave solutions of the (4+1)-dimensional Fokas equation. To solve this difficult system of nonlinear partial differential equations, we will use a new improved direct algebraic method. The given technique can be seen to work well for the purpose of converting the governing equation into a set of algebraic equations from where one can extract various traveling wave solutions. Here our results concern different forms of the solutions as solitons, periodic and rational functions. The obtained solutions are important for understanding the physical processes which are characterized by this equation and may be of use in Fluid mechanics, Nonlinear optics, Plasma physics and other areas. © 2025 NSP