Conservation laws and exact solutions of the (3+1)-dimensional Jimbo\u2013Miwa equation

Elnaz Alimirzaluo,Mehdi Nadjafikhah,Jalil Manafian

doi:10.1186/s13662-021-03578-4

Abstract

In this article, by using the Herman–Pole technique the conservation laws of the (3+1)- Jimbo–Miwa equation are obtained, and then by using the Lie symmetry analysis all of the geometric vector fields of this equation are given. Also, the non-classical symmetries of the Jimbo–Miwa equation have been determined by applying nonclassical schemes. Eventually, the ansatz solutions of the Jimbo–Miwa equations utilizing the tanh technique have been offered.

Highlights

Differential equations play a significant and key role in all sciences and disciplines; by using the analysis of these differential equations, the physical behaviors and manner of interaction and communication with the surrounding world can be discovered
By using symmetries and applying them to the group’s work field, Lie was very interested in simplifying and eliminating the ambiguities of partial differential equations (PDEs) and was able to make a great revolution in science
Lie’s group analysis method is considered as one of the systematic methods employed to achieve the nonlinear differential equations’ solutions and plays an important role in this regard [26]. This method takes a big step toward obtaining differential equations by providing the appropriate tools, and has approved its applicability by linking concepts such as conservation law and Lie’s symmetries in physics, mechanics, and other sciences [24, 25]

Summary

Introduction

Differential equations play a significant and key role in all sciences and disciplines; by using the analysis of these differential equations, the physical behaviors and manner of interaction and communication with the surrounding world can be discovered. This method takes a big step toward obtaining differential equations by providing the appropriate tools, and has approved its applicability by linking concepts such as conservation law and Lie’s symmetries in physics, mechanics, and other sciences [24, 25].

Results

Conclusion