Symmetry Analysis, Exact Solutions and Conservation Laws of a Benjamin–Bona–Mahony–Burgers Equation in 2+1-Dimensions

The Benjamin–Bona–Mahony 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–Bona–Mahony–Burgers equations depending on three arbitrary constants and an arbitrary function &l...

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Autores principales:	María S. Bruzón, Tamara M. Garrido-Letrán, Rafael de la Rosa
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	conservation laws exact solutions Lie symmetries symmetry reductions Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/de3eb7a45efd454e9ea0acfa067ac36a
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spelling	oai:doaj.org-article:de3eb7a45efd454e9ea0acfa067ac36a2021-11-25T19:06:36ZSymmetry Analysis, Exact Solutions and Conservation Laws of a Benjamin–Bona–Mahony–Burgers Equation in 2+1-Dimensions10.3390/sym131120832073-8994https://doaj.org/article/de3eb7a45efd454e9ea0acfa067ac36a2021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2083https://doaj.org/toc/2073-8994The Benjamin–Bona–Mahony 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–Bona–Mahony–Burgers equations depending on three arbitrary constants and an arbitrary function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>G</mi><mo>(</mo><mi>u</mi><mo>)</mo></mrow></semantics></math></inline-formula>. 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>G</mi><mo>′</mo></msup><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>≠</mo><mn>0</mn></mrow></semantics></math></inline-formula>, 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’s 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.María S. BruzónTamara M. Garrido-LetránRafael de la RosaMDPI AGarticleconservation lawsexact solutionsLie symmetriessymmetry reductionsMathematicsQA1-939ENSymmetry, Vol 13, Iss 2083, p 2083 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	conservation laws exact solutions Lie symmetries symmetry reductions Mathematics QA1-939
spellingShingle	conservation laws exact solutions Lie symmetries symmetry reductions Mathematics QA1-939 María S. Bruzón Tamara M. Garrido-Letrán Rafael de la Rosa Symmetry Analysis, Exact Solutions and Conservation Laws of a Benjamin–Bona–Mahony–Burgers Equation in 2+1-Dimensions
description	The Benjamin–Bona–Mahony 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–Bona–Mahony–Burgers equations depending on three arbitrary constants and an arbitrary function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>G</mi><mo>(</mo><mi>u</mi><mo>)</mo></mrow></semantics></math></inline-formula>. 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>G</mi><mo>′</mo></msup><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>≠</mo><mn>0</mn></mrow></semantics></math></inline-formula>, 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’s 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.
format	article
author	María S. Bruzón Tamara M. Garrido-Letrán Rafael de la Rosa
author_facet	María S. Bruzón Tamara M. Garrido-Letrán Rafael de la Rosa
author_sort	María S. Bruzón
title	Symmetry Analysis, Exact Solutions and Conservation Laws of a Benjamin–Bona–Mahony–Burgers Equation in 2+1-Dimensions
title_short	Symmetry Analysis, Exact Solutions and Conservation Laws of a Benjamin–Bona–Mahony–Burgers Equation in 2+1-Dimensions
title_full	Symmetry Analysis, Exact Solutions and Conservation Laws of a Benjamin–Bona–Mahony–Burgers Equation in 2+1-Dimensions
title_fullStr	Symmetry Analysis, Exact Solutions and Conservation Laws of a Benjamin–Bona–Mahony–Burgers Equation in 2+1-Dimensions
title_full_unstemmed	Symmetry Analysis, Exact Solutions and Conservation Laws of a Benjamin–Bona–Mahony–Burgers Equation in 2+1-Dimensions
title_sort	symmetry analysis, exact solutions and conservation laws of a benjamin–bona–mahony–burgers equation in 2+1-dimensions
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/de3eb7a45efd454e9ea0acfa067ac36a
work_keys_str_mv	AT mariasbruzon symmetryanalysisexactsolutionsandconservationlawsofabenjaminbonamahonyburgersequationin21dimensions AT tamaramgarridoletran symmetryanalysisexactsolutionsandconservationlawsofabenjaminbonamahonyburgersequationin21dimensions AT rafaeldelarosa symmetryanalysisexactsolutionsandconservationlawsofabenjaminbonamahonyburgersequationin21dimensions
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Symmetry Analysis, Exact Solutions and Conservation Laws of a Benjamin–Bona–Mahony–Burgers Equation in 2+1-Dimensions

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