TURK 2025

In this study, we investigate the traveling wave solutions of the Fokas equation, a notable member of the nonlinear partial differential equation family, using the Auxiliary Equation Method. By employing an appropriate wave transformation, the equation is reduced to an ordinary differential equation, facilitating the derivation of exact solutions. Through the systematic application of the Auxiliary Equation Method, we obtain a diverse set of solutions, including hyperbolic, trigonometric, and rational function forms. The physical characteristics and dynamical behaviors of these solutions are further explored through graphical representations generated using Mathematica. The results reveal that the Fokas equation exhibits a rich spectrum of traveling wave structures under different parameter settings. This study underscores the efficiency of the Auxiliary Equation Method in handling nonlinear wave equations and provides a robust analytical framework for extending the investigation to other complex nonlinear models.