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W. Hereman, A. Korpel and P. P. Banerjee, “A General Physical Approach to Solitary Wave Construction from Linear Solutions,” Wave Motion, Vol. 7, No. 3, 1985, pp. 283-289. doi:10.1016/0165-2125(85)90014-9

has been cited by the following article:

• TITLE: Expanding the Tanh-Function Method for Solving Nonlinear Equations

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

  KEYWORDS: Tanh-Function Method, Nonlinear Equations, Solitary Waves

  JOURNAL NAME: Applied Mathematics, Vol.2 No.9, September 19, 2011

  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.