Wronskian and Grammian solutions for (3+1)-dimensional Jimbo–Miwa equation

In this paper, based on the Hirota's bilinear method, the Wronskian and Grammian technique, as well as several properties of determinant, a broad set of sufficient conditions consisting of systems of linear partial differential equations are presented, which guarantees that the Wronskian determinant and the Grammian determinant solve the (3+1)-dimensional Jimbo-Miwa equation in the bilinear form, and then some special exact Wronskian and Grammian solutions are obtained by solving the differential conditions. At last, with the aid of Maple, some of these special exact solutions are shown graphically.