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

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

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...

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Main Authors: Ahmad M. Ahmad, Ashfaque H. Bokhari, F. D. Zaman
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/153817
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spelling doaj-3534106183b84d298ac195543b2bcea52020-11-24T21:46:44ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/153817153817Symmetries, Conservation Laws, and Wave Equation on the Milne MetricAhmad M. Ahmad0Ashfaque H. Bokhari1F. D. Zaman2Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi ArabiaDepartment of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi ArabiaDepartment of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi ArabiaNoether 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.http://dx.doi.org/10.1155/2012/153817
collection DOAJ
language English
format Article
sources DOAJ
author Ahmad M. Ahmad
Ashfaque H. Bokhari
F. D. Zaman
spellingShingle Ahmad M. Ahmad
Ashfaque H. Bokhari
F. D. Zaman
Symmetries, Conservation Laws, and Wave Equation on the Milne Metric
Journal of Applied Mathematics
author_facet Ahmad M. Ahmad
Ashfaque H. Bokhari
F. D. Zaman
author_sort Ahmad M. Ahmad
title Symmetries, Conservation Laws, and Wave Equation on the Milne Metric
title_short Symmetries, Conservation Laws, and Wave Equation on the Milne Metric
title_full Symmetries, Conservation Laws, and Wave Equation on the Milne Metric
title_fullStr Symmetries, Conservation Laws, and Wave Equation on the Milne Metric
title_full_unstemmed Symmetries, Conservation Laws, and Wave Equation on the Milne Metric
title_sort symmetries, conservation laws, and wave equation on the milne metric
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2012-01-01
description 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.
url http://dx.doi.org/10.1155/2012/153817
work_keys_str_mv AT ahmadmahmad symmetriesconservationlawsandwaveequationonthemilnemetric
AT ashfaquehbokhari symmetriesconservationlawsandwaveequationonthemilnemetric
AT fdzaman symmetriesconservationlawsandwaveequationonthemilnemetric
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