New periodic wave solutions of a (3+1)-dimensional Jimbo–Miwa equation

Abstract

A new three-wave method is efficient and well-developed approach to solve nonlinear partial differential equation. In this paper, a (3+1)-dimensional Jimbo-Miwa equation is investigated by using this approach. Some periodic wave solutions and kink solutions are obtained through the Hirota bilinear form. Furthermore, figures of some special periodic wave solutions and kink solutions are presented to illustrate the dynamical features of these solutions.where f = f (x, y, z, t) is also real function with respect to variables x, y, z and t. D 3x D y , D t D y and D x D z are called Hirota bilinear operators [23] defined by Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

(G'/G,1/G)-expansion method for analytical solutions of Jimbo-Miwa equation

“…Jimbo-Miwa equation was examined first by Jimbo and Miwa [31] and later by several authors. Some of these are as follows: Wazwaz has been attained multiple soliton solutions of two extended (3+1DJM) equation using the simplified Hirota's method [32], Zhang has been obtained different type solutions of (3+1DJM) equation using Hirota bilinear form [33], Ma…”