{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T22:54:20Z","timestamp":1769640860336,"version":"3.49.0"},"reference-count":44,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,8,12]],"date-time":"2022-08-12T00:00:00Z","timestamp":1660262400000},"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 present the Lie symmetry analysis for a hyperbolic partial differential system known as the one-dimensional Saint-Venant-Exner model. The model describes shallow-water systems with bed evolution given by the Exner terms. The sediment flux is considered to be a power-law function of the velocity of the fluid. The admitted Lie symmetries are classified according to the power index of the sediment flux. Furthermore, the one-dimensional optimal system is determined in all cases. From the Lie symmetries we derive similarity transformations which are applied to reduce the hyperbolic system into a set of ordinary differential equations. Closed-form exact solutions, which have not been presented before in the literature, are presented. Finally, the initial value problem for the similarity solutions is discussed.<\/jats:p>","DOI":"10.3390\/sym14081679","type":"journal-article","created":{"date-parts":[[2022,8,15]],"date-time":"2022-08-15T23:44:03Z","timestamp":1660607043000},"page":"1679","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Lie Symmetry Analysis of the One-Dimensional Saint-Venant-Exner Model"],"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":[[2022,8,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1080\/00221680309499959","article-title":"Finite volume method for simulating extreme flood events in natural channels","volume":"41","author":"Caleffi","year":"2003","journal-title":"J. Hydraul. Res."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"026314","DOI":"10.1103\/PhysRevE.82.026314","article-title":"Three-Dimensional flow in electromagnetically driven shallow two-layer fluids","volume":"82","author":"Akkermans","year":"2010","journal-title":"Phys. Rev. E"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Vallis, G.K. (2006). 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