{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:57:48Z","timestamp":1760230668010,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,8,4]],"date-time":"2022-08-04T00:00:00Z","timestamp":1659571200000},"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>We apply the theory of Lie point symmetries for the study of a family of partial differential equations which are integrable by the hyperbolic reductions method and are reduced to members of the Painlev\u00e9 transcendents. The main results of this study are that from the application of the similarity transformations provided by the Lie point symmetries, all the members of the family of the partial differential equations are reduced to second-order differential equations, which are maximal symmetric and can be linearized.<\/jats:p>","DOI":"10.3390\/sym14081603","type":"journal-article","created":{"date-parts":[[2022,8,5]],"date-time":"2022-08-05T02:12:39Z","timestamp":1659665559000},"page":"1603","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Similarity Transformations and Linearization for a Family of Dispersionless Integrable PDEs"],"prefix":"10.3390","volume":"14","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":"Instituto de Ciencias F\u00edsicas y Matem\u00e1ticas, Universidad Austral de Chile, Valdivia 5090000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"195204","DOI":"10.1088\/1751-8113\/45\/19\/195204","article-title":"On the central quadric ansatz: Integrable models and Painlev\u00e9 reductions","volume":"45","author":"Ferapontov","year":"2012","journal-title":"J. Phys. A Math. Theor."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1007\/s00220-004-1079-6","article-title":"On the integrability of (2 + 1)-dimensional quasilinear systems","volume":"248","author":"Ferapontov","year":"2004","journal-title":"Commun. Math. Phys."},{"key":"ref_3","unstructured":"Ince, E.L. (1956). 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