Automatic computation of the travelling wave solutions to nonlinear PDEs

Various extensions of the tanh-function method and their implementations for finding explicit travelling wave solutions to nonlinear partial differential equations (PDEs) have been reported in the literature. However, some solutions are often missed by these packages. In this paper, a new algorithm and its implementation called TWS for solving single nonlinear PDEs are presented. TWS is implemented in Maple 10. It turns out that, for PDEs whose balancing numbers are not positive integers, TWS works much better than existing packages. Furthermore, TWS obtains more solutions than existing packages for most cases.

• Type: Journal
• Year: 2008
• Where: CPHYSICS
• Authors: Songxin Liang, David J. Jeffrey
• Keywords: CPHYSICS 2008, Explicit Travelling, Single Nonlinear Pdes, Various Extensions