Comparative Analytical Study of Exact Traveling Wave Solutions in Nonlinear Evolution Equations via Generalized Kudryashov and Modified Simple Equation Methods

In this research, we primarily investigate two distinct methods for determining exact travelling wave solutions: The Modified Simple Equation (MSE) method and The Generalized Kudryashov method (GKM). Using the MSE method, we determined the exact travelling wave solution of the coupled (1+1) dimensional Broer-Kaup (BK) equation. Conversely, the generalized Kudryashov method was employed to find the exact travelling wave solution of the omnipotent unsteady Kortweg-de Vries (KdV) equation and its alternative, the Regularized Long Wave (RLW) equation. The solutions derived are constructed in three distinct classes: hyperbolic function, trigonometric function, and rational function structures. The accuracy of these solutions was verified with mathematical software like MAPLE. The results obtained confirm that both MSE and GKM are highly effective and valuable mathematical tools for solving various types of nonlinear evolution equations (NLEEs) in mathematical physic.