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Expanding the Tanh-Function Method for Solving Nonlinear Equations
Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
- 1 Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
- 2 Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
- 3 Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
Applied Mathematics·Volume 02 (2011)·Pages 1096–1104·Published 29 September 2011·DOI10.4236/am.2011.29151
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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.
KeywordsTanh-Function MethodNonlinear EquationsSolitary Waves
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