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

Abstract

In this paper, based on Hirota's bilinear method, the Wronskian and Grammian techniques, as well as several properties of the determinant, a broad set of sufficient conditions consisting of systems of linear partial differential equations are presented. They guarantee that the Wronskian determinant and the Grammian determinant solve the (3 + 1)-dimensional Jimbo—Miwa equation in the bilinear form. 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.

Theta Function Solutions of the 3 + 1‐Dimensional Jimbo‐Miwa Equation

“…Tang in [27] obtained its Pfaffian solution and extended Pfaffian solutions with the aid of the Hirota bilinear form. Su et al [28] constructed its Wronskian and Grammian solutions. Multiplefront solutions for (1) were obtained by employing the Hirota bilinear method in [29].…”