Novel soliton molecule solutions for the second extend (3+1)-dimensional Jimbo–Miwa equation in fluid mechanics

Abstract

Abstract The main aim of this paper is to investigate the different types of soliton molecule solutions of the second extend (3+1)-dimensional Jimbo-Miwa quation in a fluid. Four different localized waves: line solitons, breather waves, lump solutions and resonance Y-type solutions are obtained by the Hirota bilinear method directly. Furthermore, the molecule solutions consisting of only line waves, breathers or lump waves are generated by combining velocity resonance condition and long wave limit method. Also the molecule solutions such as line-breather molecule, lump-line molecule, lump-breather molecule etc.consisting of different waves are derived.
 Meanwhile, higher-order molecule solutions composed of only line waves are accquired. All of the above findings can be used to explain some natural phenomena in the ocean waves and nonlinear optics.