Backlund transformation and multiple soliton solutions for the (3+1) -dimensional Jimbo-Miwa equation

We study an approach to constructing multiple soliton solutions of the (3 + 1)- dimensional nonlinear evolution equation. We take the (3+1)-dimensional Jimbo-Miwa (JM) equation as an example. Using the extended homogeneous balance method, one can find a Backlund transformation to decompose the (3 + 1) -dimensional JM equation into a linear partial differential equation and two bilinear partial differential equations. Starting from these linear and bilinear partial differential equations, some multiple soliton solutions for the (3 + 1)-dimensional JM equation are obtained by introducing a class of formal solutions.