The tanh method : a tool for solving certain classes of nonlinear PDEsThe tanh method : a tool for solving certain classes of nonlinear PDEs
Faculty of Sciences. Physics
ICNAAM 2004: International conference on numerical analysis and applied mathematics 2004
International Conference of Numerical Analysis and Applied Mathematics, SEP 10-14, 2004, Technol Educ Inst Chalkis, Chalkis, GREECE
(2004), p. 523-525
University of Antwerp
The tanh (or hyperbolic tangent) method is a powerful technique to look for travelling waves when dealing with one-dimensional linear wave and evolution equations. In particular, this method is well suited for those problems where dispersive effects, reaction, diffusion and/or convection play an important role. Based on this method, symbolic software programs have been developed to find exact solutions. Therefore attention is focused towards examples for which these technique is used as a perturbation method. We first investigate several Boussinesq equations which arise in the field of shallow water waves. Exact as well as approximate solutions are derived. As a result, solitary wave profiles are derived. The same method can easily be extended so that difference-differential equations can be studied in the same way. (c) 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.