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 Volume 9, Number 6, 2019, Pages 2381-2388 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. PDF      Download reader