The Tanh Function Method using a Generalized Wave Transformation for Nonlinear Equations

A generalized wave transformation is suggested to transform a partial differential equation to an ordinary differential equation, the tanh function method is then used to search for exact traveling wave solutions. The combined KdV-Burgers equation with variable coefficients is used an an example to elucidate the solution procedure, the results show that this method provides straightforward and powerful mathematical tools for solving nonlinear partial differential equations in mathematical physics.