The tanh method: A tool for solving certain classes of non-linear PDEs

The tanh (or hyperbolic tangent) method is a powerful technique to look for travelling waves when dealing with one-dimensional non-linear wave and evolution equations. In particular, this method is well suited for those problems where dispersion, convection and reaction-diffusion play an important role. To show the strength of this method we study a coupled set (the so-called Boussinesq equations) which arises in the theory of non-linear dispersive water waves. As a result, a solitary wave profile is found which generalizes an earlier result, the famous Korteweg-de Vries solitary wave solution. Copyright (c) 2005 John Wiley & Sons, Ltd.