{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,15]],"date-time":"2026-02-15T21:00:26Z","timestamp":1771189226747,"version":"3.50.1"},"reference-count":37,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,22]],"date-time":"2023-01-22T00:00:00Z","timestamp":1674345600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Research Foundation of South Africa","award":["131604"],"award-info":[{"award-number":["131604"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We carried out a detailed group classification of the potential in Klein\u2013Gordon equation in anisotropic Riemannian manifolds. Specifically, we consider the Klein\u2013Gordon equations for the four-dimensional anisotropic and homogeneous spacetimes of Bianchi I, Bianchi III and Bianchi V. We derive all the closed-form expressions for the potential function where the equation admits Lie and Noether symmetries. We apply previous results which connect the Lie symmetries of the differential equation with the collineations of the Riemannian space which defines the Laplace operator, and we solve the classification problem in a systematic way.<\/jats:p>","DOI":"10.3390\/sym15020306","type":"journal-article","created":{"date-parts":[[2023,1,23]],"date-time":"2023-01-23T03:26:41Z","timestamp":1674444401000},"page":"306","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Classification of the Lie and Noether Symmetries for the Klein\u2013Gordon Equation in Anisotropic Cosmology"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9966-5517","authenticated-orcid":false,"given":"Andronikos","family":"Paliathanasis","sequence":"first","affiliation":[{"name":"Institute of Systems Science, Durban University of Technology, P.O. Box 1334, Durban 4000, South Africa"},{"name":"Departamento de Matem\u00e1ticas, Universidad Cat\u00f3lica del Norte, Avda. Angamos 0610, Antofagasta 1240000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,22]]},"reference":[{"key":"ref_1","unstructured":"Ibragimov, N.H. (2000). CRC Handbook of Lie Group Analysis of Differential Equations, Volume I: Symmetries, Exact Solutions, and Conservation Laws, CRS Press LLC."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Bluman, G.W., and Kumei, S. (1989). Symmetries of Differential Equations, Springer.","DOI":"10.1007\/978-1-4757-4307-4"},{"key":"ref_3","unstructured":"Stephani, H. (1989). Differential Equations: Their Solutions Using Symmetry, Cambridge University Press."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Olver, P.J. (1993). 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