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Vol.1, 2011
Explicit and exact non-traveling wave solutions of (3+1)-dimensional generalized shallow water equation
Jian-Guo Liu,Wen-Hui Zhu,Li Zhou,Yan He
Keywords:extended (G'/G)-expansion method, (3+1)-dimensional generalized shallow water equation, non-traveling wave solutions
Abstract:
      In this paper, a (3+1)-dimensional generalized shallow water equation is considered. New exact solutions in forms of the hyperbolic functions and the trigonometric functions are obtained based on an extended (G'/G)-expansion method and the variable separation method, which contain traveling wave solutions and non-traveling wave solutions. The particular localized excitations and the interactions between two solitary waves for these obtained exact solutions are shown in some three-dimensional graphics.