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Optimal System, Group Invariant Solutions and Conservation Laws of the Non-linear Elastic Wave Equation and Damped Elastic Wave Equation

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Title: Optimal System, Group Invariant Solutions and Conservation Laws of the Non-linear Elastic Wave Equation and Damped Elastic Wave Equation

Authors: M. Usman, A. Razzaq, Ali Raza, F.D. Zaman

Journal: Journal of Prime Research in Mathematics

HEC Recognition History
Category From To
Y 2023-07-01 2024-09-30
Y 2022-07-01 2023-06-30
Y 2021-07-01 2022-06-30
Y 2020-07-01 2021-06-30

Publisher: Abdus Salam School of Mathematical Sciences, GC University

Country: Pakistan

Year: 2023

Volume: 19

Issue: 1

Language: English

Keywords: Conservation lawsNon-linear elastic wave equationLie symmetriesOptimal systemGroup invariant solutions

Categories
Elasticity (6) Lie Symmetry Analysis (1) Conservation Laws (1) Nonlinear Waves (3) Differential Equations (206)

Abstract

Non-linear wave equations are created by the elastic wave propagation through inelastic material. We obtain the Lie point symmetries for the non-linear elastic wave equation and the optimal system of the symmetry algebra using Lie symmetry approach. Numerous solutions that are group invariant are obtained under the optimal system of subalgebras of Lie algebra. Additionally, the variational symmetries are obtained via Noether approach and the corresponsing conservation laws are presented. The non-linear elastic wave equation with a damping term is also studied. The local conservation laws using the direct approach are also discussed in this study.

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