{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:37:34Z","timestamp":1753886254548,"version":"3.41.2"},"reference-count":13,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,12,30]],"date-time":"2012-12-30T00:00:00Z","timestamp":1356825600000},"content-version":"vor","delay-in-days":364,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"King Fahd University"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>Noether symmetries provide conservation laws that are admitted by Lagrangians\nrepresenting 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.<\/jats:p>","DOI":"10.1155\/2012\/153817","type":"journal-article","created":{"date-parts":[[2012,12,30]],"date-time":"2012-12-30T21:01:49Z","timestamp":1356901309000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Symmetries, Conservation Laws, and Wave Equation on the Milne Metric"],"prefix":"10.1155","volume":"2012","author":[{"given":"Ahmad M.","family":"Ahmad","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ashfaque H.","family":"Bokhari","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"F. 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Applications of the theory of evolution equations to general relativityin General Relativity Proceedings of the 16th International Conference 2002 Singapore World Scientific.","DOI":"10.1142\/9789812776556_0014"},{"volume-title":"Symmetry and Integration Methods for Differential Equations","year":"2002","author":"Bluman G. W.","key":"e_1_2_6_8_2"},{"key":"e_1_2_6_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4307-4"},{"volume-title":"Introduction to Symmetry Analysis","year":"2002","author":"Cantwell B. J.","key":"e_1_2_6_10_2"},{"key":"e_1_2_6_11_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511623967"},{"key":"e_1_2_6_12_2","article-title":"Symmetries, conservation laws and reduction of wave and Gordon-type equations on Riemannian manifolds","volume":"60","author":"Jamal S.","year":"2011","journal-title":"World Academy of Science, Engineering and Technology"},{"volume-title":"Gravitation","year":"1973","author":"Misner C. 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