Constructing Exact Solutions of the Burgers-Huxley Equation via (G'/G) -Expansion Method

Abstract

This study derives exact analytical solutions to the Burgers–Huxley equation by employing the extended (G'/G)-expansion method. By applying the traveling wave transformation: , the nonlinear partial differential equation is reduced to an ordinary differential equation. The method is based on a finite expansion in terms of (G'/G), where the order of expansion is determined using the homogeneous balance principle. Substitution into the reduced equation generates a system of algebraic equations for the unknown parameters, whose solutions yield several classes of exact traveling wave solutions. These solutions are expressed in hyperbolic, trigonometric, and rational functional forms, and can be categorized into distinct nonlinear wave structures, including solitary waves and kink-type solutions. The kink-type solutions characterize transition waves connecting two different asymptotic states, whereas the solitary wave solutions represent localized, stable structures. The obtained results highlight the effectiveness of the Extended -expansion method in constructing diverse families of exact solutions for nonlinear evolution equations.