Expanding the Tanh-Function Method for Solving Nonlinear Equations

Nassar Hassan Abdel-Aal, Mohamed Abdullah Abdel-Razek, Abdullah Kamel Seddeek

Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt.

DOI: 10.4236/am.2011.29151                

Abstract

In this paper, using the tanh-function method, we introduce a new approach to solitary wave solutions for solving nonlinear PDEs. The proposed method is based on adding integration constants to the resulting nonlinear ODEs from the nonlinear PDEs using the wave transformation. Also, we use a transformation related to those integration constants. Some examples are considered to find their exact solutions such as KdV- Burgers class and Fisher, Boussinesq and Klein-Gordon equations. Moreover, we discuss the geometric interpretations of the resulting exact solutions.

Keywords

Tanh-Function Method, Nonlinear Equations, Solitary Waves

Conflicts of Interest

The authors declare no conflicts of interest.

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