Abstract

In this paper, by using bilinear form and extended  three-wave type of ans$\ddot{a}$tz approach, we obtain new multi-soliton  solutions of the (3+1)-dimensional  Jimbo-Miwa  equation, including the periodic breather-type of kink three-soliton  solutions, the cross-kink four-soliton solutions, the doubly periodic breather-type of soliton solutions and the doubly periodic breather-type of cross-kink two-soliton  solutions. 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.

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