Exact solutions of the (3+1)-dimensional Jimbo-Miwa equation via Wronskian solutions: Soliton, breather, and multiple lump solutions

Abstract

In this paper, the Hirota bilinear method is applied to investigate the exact solutions of the (3+1)-dimensional Jimbo-Miwa (JM) equation, including solitons, breathers and lumps, which satisfy specific Wronskian conditions. Their dynamic behaviors and the effects of free parameters on the propagation direction and velocity are analyzed through three-dimensional images and the corresponding contour plots. Especially, based on the 2Mth-order Wronskian determinant solutions, the determinant expression of arbitrary Mth-order lump solutions is constructed by employing elementary transformation and long wave limit. The experimental results show that the interaction between multiple lumps is a completely elastic collision. These results may be helpful to understand the propagation processes of nonlinear waves in some nonlinear physical systems, such as fluid mechanics, nonlinear optics and so on.