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Taogetusang, S. (2006) New Type of Exact Solitary Wave Solutions for Dispersive Long- Wave Equation and Benjamin Equation.

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• TITLE: Exact Solutions of Gardner Equations through tanh-coth Method

  AUTHORS: Lin Lin, Shiyong Zhu, Yinkang Xu, Yubing Shi

  KEYWORDS: tanh-coth Method, Gardner Equations, Soliton Solutions

  JOURNAL NAME: Applied Mathematics, Vol.7 No.18, December 22, 2016

  ABSTRACT: In this paper, we apply the tanh-coth method and traveling wave transformation method for solving Gardner equations, including (1 + 1)-Gardner and (2 + 1)- Gardner equations. The tanh-coth method proved to be reliable and effective in handling a large number of nonlinear dispersive and disperse equations. Through tanh-coth method, we get analytical expressions of soliton solutions of Gardner equations. The one-soliton solution is characterized by an infinite wing or infinite tail.