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The three-wave method for two shallow water wave equations

In this paper, two shallow water wave equations are studied by extended three-soliton method. The new exact solutions including the kink-soliton solution, the anti-kink soliton solution, the distortional solitary wave solution and smooth solitary wave solution for the shallow water wave equations are obtained. Their dynamic properties of some exact solutions are discussed and their profiles of these solutions are given by use of software Maple.