On the Symmetries and Conservation Laws of the Multidimensional Nonlinear Damped Wave Equations

Usamah S. Al-Ali; Ashfaque H. Bokhari; A. H. Kara; F. D. Zaman

doi:10.1155/2017/9401205

Advances in Mathematical Physics (Jan 2017)

On the Symmetries and Conservation Laws of the Multidimensional Nonlinear Damped Wave Equations

Usamah S. Al-Ali,
Ashfaque H. Bokhari,
A. H. Kara,
F. D. Zaman

Affiliations

Usamah S. Al-Ali: Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Ashfaque H. Bokhari: Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
A. H. Kara: School of Mathematics, University of the Witwatersrand, Johannesburg, Wits 2050, South Africa
F. D. Zaman: Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

DOI: https://doi.org/10.1155/2017/9401205
Journal volume & issue: Vol. 2017

Abstract

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We carry out a classification of Lie symmetries for the (2+1)-dimensional nonlinear damped wave equation utt+fuut=div(gugrad u) with variable damping. Similarity reductions of the equation are performed using the admitted Lie symmetries of the equation and some interesting solutions are presented. Employing the multiplier approach, admitted conservation laws of the equation are constructed for some new, interesting cases.

Published in Advances in Mathematical Physics

ISSN: 1687-9120 (Print); 1687-9139 (Online)
Publisher: Hindawi Limited
Country of publisher: United Kingdom
LCC subjects: Science: Physics
Website: https://onlinelibrary.wiley.com/journal/3197

About the journal