On the dynamics of localized excitation wave solutions to an extended (3+1)-dimensional Jimbo–Miwa equation

Abstract

Three types of localized excitation structures, including multi-dromion, multi-lump and periodic solutions, for the extended (3+1)-dimensional Jimbo–Miwa equation are constructed based on Hirota bilinear and variable separation methods. By adding constraint conditions to make the velocities equal or not, a bound state solution can be obtained, which demonstrates chase collision and interesting interaction phenomena. Especially, their dynamic characteristics are analyzed in detail and vividly displayed.