{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T10:59:10Z","timestamp":1760785150829,"version":"build-2065373602"},"reference-count":64,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,8,2]],"date-time":"2023-08-02T00:00:00Z","timestamp":1690934400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A detailed symmetry analysis is performed for a microscopic model used to describe traffic flow in two-lane motorways. The traffic flow theory employed in this model is a two-dimensional extension of the Aw-Rascle theory. The flow parameters, including vehicle density, and vertical and horizontal velocities, are described by a system of first-order partial differential equations belonging to the family of hydrodynamic systems. This fluid-dynamics model is expressed in terms of the Euler and Lagrange variables. The admitted Lie point symmetries and the one-dimensional optimal system are determined for both sets of variables. It is found that the admitted symmetries for the two sets of variables form different Lie algebras, leading to distinct one-dimensional optimal systems. Finally, the Lie symmetries are utilized to derive new similarity closed-form solutions.<\/jats:p>","DOI":"10.3390\/sym15081525","type":"journal-article","created":{"date-parts":[[2023,8,2]],"date-time":"2023-08-02T11:04:38Z","timestamp":1690974278000},"page":"1525","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Symmetry Analysis for the 2D Aw-Rascle Traffic-Flow Model of Multi-Lane Motorways in the Euler and Lagrange Variables"],"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, Casilla, Antofagasta 1280, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,2]]},"reference":[{"key":"ref_1","unstructured":"Lie, S. (1970). Theorie der Transformationsgrupprn: Volume I, Chelsea."},{"key":"ref_2","unstructured":"Lie, S. (1970). Theorie der Transformationsgrupprn: Volume II, Chelsea."},{"key":"ref_3","unstructured":"Lie, S. (1970). Theorie der Transformationsgrupprn: Volume III, Chelsea."},{"key":"ref_4","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_5","doi-asserted-by":"crossref","unstructured":"Ovsiannikov, L.V. (1982). 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