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

✍ Scribed by W. Malfliet

• Publisher: John Wiley and Sons
• Year: 2005
• Tongue: English
• Weight: 60 KB
• Volume: 28
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.650

✦ Synopsis

Abstract

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 © 2005 John Wiley & Sons, Ltd.