Bounded and unbounded traveling wave solutions of the (3+1)-dimensional Jimbo-Miwa equation

Abstract

This paper studies traveling waves of the (3+1)-dimensional Jimbo-Miwa equation comprehensively and systematically. By transforming its traveling wave system into a dynamical system in R3, we apply the bifurcation method of dynamical system to investigate its phase space geometry in detail and obtain the parameter bifurcation sets in which various types of bounded and unbounded traveling waves are identified and simulated. Furthermore, by calculating the complicated elliptic integrals, without any loss, we give exact expressions of all traveling wave solutions of the (3+1)-dimensional Jimbo-Miwa equation, including the bounded and unbounded ones. Keywords: Jimbo-Miwa equation, Traveling waves, Dynamical system, Bifurcation, Elliptic integral