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Abstract: In this paper, the (3+1)-dimensional potential-YTSF equation is investigated. Exact solutions with three-wave form including periodic cross-kink wave, periodic two-solitary wave and breather type of two-solitary wave solutions are obtained using Hirota’s bilinear form and generalized three-wave approach with the aid of symbolic computation. Moreover, the properties for some new solutions are shown with some figures. [Copyright &y& Elsevier]

Abstract: Exact three-wave solutions including periodic cross-kink wave solutions, doubly periodic solitary wave solutions and breather type of two-solitary wave solutions for the (3+1)-dimensional Jimbo–Miwa equation are obtained using the generalized three-wave method. It is shown that the generalized three-wave method, with the help of symbolic computation, provides an effective and powerful mathematical tool for solving high-dimensional nonlinear evolution equations in mathematical physics. [Copyright &y& Elsevier]

Abstract: New exact solutions including the kink-shaped solutions, bell-shaped solutions, periodic solutions, singular soliton solutions and rational solution for the (2+1)-dimensional Sine-Gordon equation are obtained using the tanh method, the -expansion method and the auxiliary function method, respectively. [Copyright &y& Elsevier]