Invariance properties and conservation laws of the nonlinear damped wave equation with power law nonlinearities

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

Results in Physics (Jan 2017)

Invariance properties and conservation laws of the nonlinear damped wave equation with power law nonlinearities

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, Saudi Arabia
Ashfaque H. Bokhari: Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia; Corresponding author.
A.H. Kara: Permanent address: School of Mathematics, University of the Witwatersrand, Johannesburg, Wits, 2050, South Africa; Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
F.D. Zaman: Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

Journal volume & issue: Vol. 7
pp. 991 – 994

Abstract

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Nonlinear evolution equations represent some of the most fundamental processes in both physics as well engineering. Considering this, we analyze and classify the three dimensional wave equation with a power law nonlinearity in presence of damping and external force terms. In view of the significance of conservation laws in physics, a study of the invariance properties is presented and conservation laws are constructed and classified. An illustrative case of a symmetry reduction in one special case is presented. Keywords: Power law non-linearity, Diffusion, Damped wave, Conservation laws

Published in Results in Physics

ISSN: 2211-3797 (Online)
Publisher: Elsevier
Country of publisher: Netherlands
LCC subjects: Science: Physics
Website: http://www.journals.elsevier.com/results-in-physics/

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