{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T19:00:43Z","timestamp":1768417243679,"version":"3.49.0"},"reference-count":44,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,11,3]],"date-time":"2021-11-03T00:00:00Z","timestamp":1635897600000},"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>The Benjamin\u2013Bona\u2013Mahony equation describes the unidirectional propagation of small-amplitude long waves on the surface of water in a channel. In this paper, we consider a family of generalized Benjamin\u2013Bona\u2013Mahony\u2013Burgers equations depending on three arbitrary constants and an arbitrary function G(u). We study this family from the standpoint of the theory of symmetry reductions of partial differential equations. Firstly, we obtain the Lie point symmetries admitted by the considered family. Moreover, taking into account the admitted point symmetries, we perform symmetry reductions. In particular, for G\u2032(u)\u22600, we construct an optimal system of one-dimensional subalgebras for each maximal Lie algebra and deduce the corresponding (1+1)-dimensional nonlinear third-order partial differential equations. Then, we apply Kudryashov\u2019s method to look for exact solutions of the nonlinear differential equation. We also determine line soliton solutions of the family of equations in a particular case. Lastly, through the multipliers method, we have constructed low-order conservation laws admitted by the family of equations.<\/jats:p>","DOI":"10.3390\/sym13112083","type":"journal-article","created":{"date-parts":[[2021,11,3]],"date-time":"2021-11-03T21:57:49Z","timestamp":1635976669000},"page":"2083","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Symmetry Analysis, Exact Solutions and Conservation Laws of a Benjamin\u2013Bona\u2013Mahony\u2013Burgers Equation in 2+1-Dimensions"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3599-6106","authenticated-orcid":false,"given":"Mar\u00eda","family":"Bruz\u00f3n","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Facultad de Ciencias, Universidad de C\u00e1diz, 11510 Puerto Real, C\u00e1diz, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9536-1065","authenticated-orcid":false,"given":"Tamara","family":"Garrido-Letr\u00e1n","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Facultad de Ciencias, Universidad de C\u00e1diz, 11510 Puerto Real, C\u00e1diz, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9357-9167","authenticated-orcid":false,"given":"Rafael","family":"de la Rosa","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Facultad de Ciencias, Universidad de C\u00e1diz, 11510 Puerto Real, C\u00e1diz, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,3]]},"reference":[{"key":"ref_1","first-page":"47","article-title":"Model Equations for Long Waves in Nonlinear Dispersive Systems","volume":"272","author":"Benjamin","year":"1972","journal-title":"Phil. 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