Exact three-wave solutions for the (3+1)(3+1)-dimensional Jimbo–Miwa equation

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.