Lie symmetry analysis, optimal system, and new exact solutions of a (3 + 1) dimensional nonlinear evolution equation

Studies on Non-linear evolutionary equations have become more critical as time evolves. Such equations are not far-fetched in fluid mechanics, plasma physics, optical fibers, and other scientific applications. It should be an essential aim to find exact solutions of these equations. In this work, th...

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Autores principales:	Tiwari Ashish, Sharma Kajal, Arora Rajan
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	(3 + 1) - dimensional nonlinear evolution equation optimal system lie symmetry analysis group invariant solutions Engineering (General). Civil engineering (General) TA1-2040
Acceso en línea:	https://doaj.org/article/21ed564d56624866b2470f901bb0a2bb
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spelling	oai:doaj.org-article:21ed564d56624866b2470f901bb0a2bb2021-12-05T14:10:57ZLie symmetry analysis, optimal system, and new exact solutions of a (3 + 1) dimensional nonlinear evolution equation2192-80102192-802910.1515/nleng-2021-0010https://doaj.org/article/21ed564d56624866b2470f901bb0a2bb2021-06-01T00:00:00Zhttps://doi.org/10.1515/nleng-2021-0010https://doaj.org/toc/2192-8010https://doaj.org/toc/2192-8029Studies on Non-linear evolutionary equations have become more critical as time evolves. Such equations are not far-fetched in fluid mechanics, plasma physics, optical fibers, and other scientific applications. It should be an essential aim to find exact solutions of these equations. In this work, the Lie group theory is used to apply the similarity reduction and to find some exact solutions of a (3+1) dimensional nonlinear evolution equation. In this report, the groups of symmetries, Tables for commutation, and adjoints with infinitesimal generators were established. The subalgebra and its optimal system is obtained with the aid of the adjoint Table. Moreover, the equation has been reduced into a new PDE having less number of independent variables and at last into an ODE, using subalgebras and their optimal system, which gives similarity solutions that can represent the dynamics of nonlinear waves.Tiwari AshishSharma KajalArora RajanDe Gruyterarticle(3 + 1) - dimensional nonlinear evolution equationoptimal systemlie symmetry analysisgroup invariant solutionsEngineering (General). Civil engineering (General)TA1-2040ENNonlinear Engineering, Vol 10, Iss 1, Pp 132-145 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	(3 + 1) - dimensional nonlinear evolution equation optimal system lie symmetry analysis group invariant solutions Engineering (General). Civil engineering (General) TA1-2040
spellingShingle	(3 + 1) - dimensional nonlinear evolution equation optimal system lie symmetry analysis group invariant solutions Engineering (General). Civil engineering (General) TA1-2040 Tiwari Ashish Sharma Kajal Arora Rajan Lie symmetry analysis, optimal system, and new exact solutions of a (3 + 1) dimensional nonlinear evolution equation
description	Studies on Non-linear evolutionary equations have become more critical as time evolves. Such equations are not far-fetched in fluid mechanics, plasma physics, optical fibers, and other scientific applications. It should be an essential aim to find exact solutions of these equations. In this work, the Lie group theory is used to apply the similarity reduction and to find some exact solutions of a (3+1) dimensional nonlinear evolution equation. In this report, the groups of symmetries, Tables for commutation, and adjoints with infinitesimal generators were established. The subalgebra and its optimal system is obtained with the aid of the adjoint Table. Moreover, the equation has been reduced into a new PDE having less number of independent variables and at last into an ODE, using subalgebras and their optimal system, which gives similarity solutions that can represent the dynamics of nonlinear waves.
format	article
author	Tiwari Ashish Sharma Kajal Arora Rajan
author_facet	Tiwari Ashish Sharma Kajal Arora Rajan
author_sort	Tiwari Ashish
title	Lie symmetry analysis, optimal system, and new exact solutions of a (3 + 1) dimensional nonlinear evolution equation
title_short	Lie symmetry analysis, optimal system, and new exact solutions of a (3 + 1) dimensional nonlinear evolution equation
title_full	Lie symmetry analysis, optimal system, and new exact solutions of a (3 + 1) dimensional nonlinear evolution equation
title_fullStr	Lie symmetry analysis, optimal system, and new exact solutions of a (3 + 1) dimensional nonlinear evolution equation
title_full_unstemmed	Lie symmetry analysis, optimal system, and new exact solutions of a (3 + 1) dimensional nonlinear evolution equation
title_sort	lie symmetry analysis, optimal system, and new exact solutions of a (3 + 1) dimensional nonlinear evolution equation
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/21ed564d56624866b2470f901bb0a2bb
work_keys_str_mv	AT tiwariashish liesymmetryanalysisoptimalsystemandnewexactsolutionsofa31dimensionalnonlinearevolutionequation AT sharmakajal liesymmetryanalysisoptimalsystemandnewexactsolutionsofa31dimensionalnonlinearevolutionequation AT arorarajan liesymmetryanalysisoptimalsystemandnewexactsolutionsofa31dimensionalnonlinearevolutionequation
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Lie symmetry analysis, optimal system, and new exact solutions of a (3 + 1) dimensional nonlinear evolution equation

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