{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T04:24:48Z","timestamp":1772598288865,"version":"3.50.1"},"reference-count":29,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,10,12]],"date-time":"2023-10-12T00:00:00Z","timestamp":1697068800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Research Foundation of South Africa"},{"name":"University of KwaZulu-Natal"},{"name":"Durban University of Technology"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The magnetohydrodynamics (1 + 1) dimension equation, with a force and force-free term, is analysed with respect to its point symmetries. Interestingly, it reduces to an Abel\u2019s Equation of the second kind and, under certain conditions, to equations specified in Gambier\u2019s family. The symmetry analysis for the force-free term leads to Euler\u2019s Equation and to a system of reduced second-order odes for which singularity analysis is performed to determine their integrability.<\/jats:p>","DOI":"10.3390\/sym15101908","type":"journal-article","created":{"date-parts":[[2023,10,12]],"date-time":"2023-10-12T07:28:44Z","timestamp":1697095724000},"page":"1908","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Solutions of Magnetohydrodynamics Equation through Symmetries"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7891-3860","authenticated-orcid":false,"given":"Rangasamy","family":"Sinuvasan","sequence":"first","affiliation":[{"name":"Department of Mathematics, VIT-AP University, Amaravati 522237, Andhra Pradesh, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9845-4697","authenticated-orcid":false,"given":"Amlan K.","family":"Halder","sequence":"additional","affiliation":[{"name":"School of Technology, Woxsen University, Hyderabad 502345, Telangana, India"}]},{"given":"Rajeswari","family":"Seshadri","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Pondicherry University, Puducherry 605014, Kalapet, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9966-5517","authenticated-orcid":false,"given":"Andronikos","family":"Paliathanasis","sequence":"additional","affiliation":[{"name":"Institute of Systems Science, Durban University of Technology, Durban 4000, South Africa"},{"name":"Departamento de Matem\u00e1ticas, Universidad Cat\u00f3lica del Norte, Avda. Angamos 0610, Casilla, Antofagasta 1280, Chile"}]},{"given":"Peter G. L.","family":"Leach","sequence":"additional","affiliation":[{"name":"Institute of Systems Science, Durban University of Technology, Durban 4000, South Africa"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"R2709","DOI":"10.1103\/PhysRevE.58.R2709","article-title":"Compressible Alfven turbulence in one dimension","volume":"58","author":"Fleischer","year":"1998","journal-title":"Phys. Rev. E"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"636","DOI":"10.1103\/PhysRevE.52.636","article-title":"Model of intermittency in magnetohydrodynamic turbulence","volume":"52","author":"Politano","year":"1995","journal-title":"Phys. Rev. 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