Symmetry Solutions and Conservation Laws for the 3D Generalized Potential Yu-Toda-Sasa-Fukuyama Equation of Mathematical Physics

Chaudry Masood Khalique,Oageng Lawrence Diteho,Karabo Plaatjie

doi:10.3390/sym13112058

Chaudry Masood Khalique, Oageng Lawrence Diteho + Show 1 more

Open Access

https://doi.org/10.3390/sym13112058

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Journal: Symmetry	Publication Date: Nov 1, 2021
Citations: 2	License type: CC BY 4.0

Affiliation: Azerbaijan University, North-West University

Abstract

In this paper we study the fourth-order three-dimensional generalized potential Yu-Toda-Sasa-Fukuyama (gpYTSF) equation by first computing its Lie point symmetries and then performing symmetry reductions. The resulting ordinary differential equations are then solved using direct integration, and exact solutions of gpYTSF equation are obtained. The obtained group invariant solutions include the solution in terms of incomplete elliptic integral. Furthermore, conservation laws for the gpYTSF equation are derived using both the multiplier and Noether’s methods. The multiplier method provides eight conservation laws, while the Noether’s theorem supplies seven conservation laws. These conservation laws include the conservation of energy and mass.

Highlights

Many natural phenomena of the real world are modelled using nonlinear partial differential equations (NPDEs)
We studied the fourth-order three-dimensional generalized potential YuToda-Sasa-Fukuyama Equation (2)
The group invariant solutions obtained included a solution in terms of incomplete elliptic integral

Summary

Introduction

Many natural phenomena of the real world are modelled using nonlinear partial differential equations (NPDEs). There have been several studies done on NPDEs and many researchers have suggested various techniques for finding exact solutions for such equations, since there is no general theory that can be applied to find exact solutions These techniques include the Jacobi elliptic function expansion method [1], the homogeneous balance method [2], the Kudryashov’s method [3], the ansatz method [4], the inverse scattering transform method [5], the Backlund transformation [6], the Darboux transformation [7], the Hirota bilinear method [8], the (G /G)−expansion method [9], and the Lie symmetry method [10,11,12,13,14,15], just to mention a few. Exact solutions that included lump solutions and interaction solutions of (1) were obtained using the generalized Hirota bilinear method [34]. Conserved quantities of Equation (2) are established using two approaches: multiplier approach and Noether’s approach

Lie Point Symmetries

Solution via the Incomplete Elliptic Integral

Conservation Laws Using the Multiplier Approach

Conservation Laws Using Noether’s Approach

Conclusions