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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 153817, 7 pages
http://dx.doi.org/10.1155/2012/153817
Research Article

Symmetries, Conservation Laws, and Wave Equation on the Milne Metric

Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Received 2 September 2012; Revised 27 November 2012; Accepted 27 November 2012

Academic Editor: Fazal M. Mahomed

Copyright © 2012 Ahmad M. Ahmad et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Noether symmetries provide conservation laws that are admitted by Lagrangians representing physical systems. For partial differential equation possessing Lagrangians these symmetries are obtained by the invariance of the corresponding action integral. In this paper we provide a systematic procedure for determining Noether symmetries and conserved vectors for a Lagrangian constructed from a Lorentzian metric of interest in mathematical physics. For completeness, we give Lie point symmetries and conservation laws admitted by the wave equation on this Lorentzian metric.