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

Abstract

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.