Exact solutions, Lagrangians and first integrals for generalized Camassa–Holm equation

In this paper, Lagrangians and the first integrals of a new class of Liénard-type equations have been investigated. This class can be obtained using the traveling wave reduction of the generalized Camassa–Holm equation. This task is achieved using the direct definitions of the Lagrangians and first...

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Autores principales:	H. Elzehri, A.H. Abdel Kader, M.S. Abdel Latif
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Liénard-type equations Solitons Doubly periodic solutions Applied mathematics. Quantitative methods T57-57.97
Acceso en línea:	https://doaj.org/article/2e405306e1e34b20a79338f01ed079e6
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spelling	oai:doaj.org-article:2e405306e1e34b20a79338f01ed079e62021-11-04T04:43:10ZExact solutions, Lagrangians and first integrals for generalized Camassa–Holm equation2666-818110.1016/j.padiff.2021.100176https://doaj.org/article/2e405306e1e34b20a79338f01ed079e62021-12-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2666818121000929https://doaj.org/toc/2666-8181In this paper, Lagrangians and the first integrals of a new class of Liénard-type equations have been investigated. This class can be obtained using the traveling wave reduction of the generalized Camassa–Holm equation. This task is achieved using the direct definitions of the Lagrangians and first integrals. Infinite standard and non-standard Lagrangians are obtained for this class of equations. Some autonomous and nonautonomous first integrals for this class of equations have been obtained. The obtained Lagrangians and first integrals are new. Also, using the obtained first integrals, we have obtained some new exact solutions for the generalized Camassa–Holm equation. The obtained solutions are doubly periodic, dark, and bright soliton solutions which are very important in interpreting physical phenomena modeled using the generalized Camassa–Holm equation.H. ElzehriA.H. Abdel KaderM.S. Abdel LatifElsevierarticleLiénard-type equationsSolitonsDoubly periodic solutionsApplied mathematics. Quantitative methodsT57-57.97ENPartial Differential Equations in Applied Mathematics, Vol 4, Iss , Pp 100176- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Liénard-type equations Solitons Doubly periodic solutions Applied mathematics. Quantitative methods T57-57.97
spellingShingle	Liénard-type equations Solitons Doubly periodic solutions Applied mathematics. Quantitative methods T57-57.97 H. Elzehri A.H. Abdel Kader M.S. Abdel Latif Exact solutions, Lagrangians and first integrals for generalized Camassa–Holm equation
description	In this paper, Lagrangians and the first integrals of a new class of Liénard-type equations have been investigated. This class can be obtained using the traveling wave reduction of the generalized Camassa–Holm equation. This task is achieved using the direct definitions of the Lagrangians and first integrals. Infinite standard and non-standard Lagrangians are obtained for this class of equations. Some autonomous and nonautonomous first integrals for this class of equations have been obtained. The obtained Lagrangians and first integrals are new. Also, using the obtained first integrals, we have obtained some new exact solutions for the generalized Camassa–Holm equation. The obtained solutions are doubly periodic, dark, and bright soliton solutions which are very important in interpreting physical phenomena modeled using the generalized Camassa–Holm equation.
format	article
author	H. Elzehri A.H. Abdel Kader M.S. Abdel Latif
author_facet	H. Elzehri A.H. Abdel Kader M.S. Abdel Latif
author_sort	H. Elzehri
title	Exact solutions, Lagrangians and first integrals for generalized Camassa–Holm equation
title_short	Exact solutions, Lagrangians and first integrals for generalized Camassa–Holm equation
title_full	Exact solutions, Lagrangians and first integrals for generalized Camassa–Holm equation
title_fullStr	Exact solutions, Lagrangians and first integrals for generalized Camassa–Holm equation
title_full_unstemmed	Exact solutions, Lagrangians and first integrals for generalized Camassa–Holm equation
title_sort	exact solutions, lagrangians and first integrals for generalized camassa–holm equation
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/2e405306e1e34b20a79338f01ed079e6
work_keys_str_mv	AT helzehri exactsolutionslagrangiansandfirstintegralsforgeneralizedcamassaholmequation AT ahabdelkader exactsolutionslagrangiansandfirstintegralsforgeneralizedcamassaholmequation AT msabdellatif exactsolutionslagrangiansandfirstintegralsforgeneralizedcamassaholmequation
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Exact solutions, Lagrangians and first integrals for generalized Camassa–Holm equation

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