Enhanced Hyperbolic Tangent (Tanh) Method for Solving Nonlinear Wave Equation Systems

Abstract

This work investigates the use of the enhanced hyperbolic tangent (tanh) method combined with symbolic computation via Maple to solve nonlinear wave equation systems. The study focuses on exact traveling wave solutions for equations including the Burgers equation, classical and coupled Korteweg–de Vries (KdV) equations, and the coupled Hirota–Satsuma system. By applying the extended tanh method, nonlinear partial differential equations are transformed into algebraic systems that can be solved to obtain various exact solutions such as solitons, kinks, solitary waves, and periodic solutions. Maple 17 is utilized to handle the intensive symbolic computations involved. The results demonstrate the effectiveness and wide applicability of the enhanced tanh method in analyzing nonlinear wave phenomena and solving complex nonlinear PDEs in mathematical physics.