Exact Solutions and Conservation Laws of a Generalized (1 + 1) Dimensional System of Equations via Symbolic Computation

The aim of this paper is to compute the exact solutions and conservation of a generalized (1 + 1) dimensional system. This can be achieved by employing symbolic manipulation software such as Maple, Mathematica, or MATLAB. In theoretical physics and in many scientific applications, the mentioned syst...

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Autores principales:	Sivenathi Oscar Mbusi, Ben Muatjetjeja, Abdullahi Rashid Adem
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	auxiliary equations associated solutions Lie symmetry analysis conservation laws Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/f2647f026b4240b09883932b02499085
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spelling	oai:doaj.org-article:f2647f026b4240b09883932b024990852021-11-25T18:17:11ZExact Solutions and Conservation Laws of a Generalized (1 + 1) Dimensional System of Equations via Symbolic Computation10.3390/math92229162227-7390https://doaj.org/article/f2647f026b4240b09883932b024990852021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2916https://doaj.org/toc/2227-7390The aim of this paper is to compute the exact solutions and conservation of a generalized (1 + 1) dimensional system. This can be achieved by employing symbolic manipulation software such as Maple, Mathematica, or MATLAB. In theoretical physics and in many scientific applications, the mentioned system naturally arises. Time, space, and scaling transformation symmetries lead to novel similarity reductions and new exact solutions. The solutions obtained include solitary waves and cnoidal and snoidal waves. The familiarity of closed-form solutions of nonlinear ordinary and partial differential equations enables numerical solvers and supports stability analysis. Although many efforts have been dedicated to solving nonlinear evolution equations, there is no unified method. To the best of our knowledge, this is the first time that Lie point symmetry analysis in conjunction with an ansatz method has been applied on this underlying equation. It should also be noted that the methods applied in this paper give a unique solution set that differs from the newly reported solutions. In addition, we derive the conservation laws of the underlying system. It is also worth mentioning that this is the first time that the conservation laws for the equation under study are derived.Sivenathi Oscar MbusiBen MuatjetjejaAbdullahi Rashid AdemMDPI AGarticleauxiliary equationsassociated solutionsLie symmetry analysisconservation lawsMathematicsQA1-939ENMathematics, Vol 9, Iss 2916, p 2916 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	auxiliary equations associated solutions Lie symmetry analysis conservation laws Mathematics QA1-939
spellingShingle	auxiliary equations associated solutions Lie symmetry analysis conservation laws Mathematics QA1-939 Sivenathi Oscar Mbusi Ben Muatjetjeja Abdullahi Rashid Adem Exact Solutions and Conservation Laws of a Generalized (1 + 1) Dimensional System of Equations via Symbolic Computation
description	The aim of this paper is to compute the exact solutions and conservation of a generalized (1 + 1) dimensional system. This can be achieved by employing symbolic manipulation software such as Maple, Mathematica, or MATLAB. In theoretical physics and in many scientific applications, the mentioned system naturally arises. Time, space, and scaling transformation symmetries lead to novel similarity reductions and new exact solutions. The solutions obtained include solitary waves and cnoidal and snoidal waves. The familiarity of closed-form solutions of nonlinear ordinary and partial differential equations enables numerical solvers and supports stability analysis. Although many efforts have been dedicated to solving nonlinear evolution equations, there is no unified method. To the best of our knowledge, this is the first time that Lie point symmetry analysis in conjunction with an ansatz method has been applied on this underlying equation. It should also be noted that the methods applied in this paper give a unique solution set that differs from the newly reported solutions. In addition, we derive the conservation laws of the underlying system. It is also worth mentioning that this is the first time that the conservation laws for the equation under study are derived.
format	article
author	Sivenathi Oscar Mbusi Ben Muatjetjeja Abdullahi Rashid Adem
author_facet	Sivenathi Oscar Mbusi Ben Muatjetjeja Abdullahi Rashid Adem
author_sort	Sivenathi Oscar Mbusi
title	Exact Solutions and Conservation Laws of a Generalized (1 + 1) Dimensional System of Equations via Symbolic Computation
title_short	Exact Solutions and Conservation Laws of a Generalized (1 + 1) Dimensional System of Equations via Symbolic Computation
title_full	Exact Solutions and Conservation Laws of a Generalized (1 + 1) Dimensional System of Equations via Symbolic Computation
title_fullStr	Exact Solutions and Conservation Laws of a Generalized (1 + 1) Dimensional System of Equations via Symbolic Computation
title_full_unstemmed	Exact Solutions and Conservation Laws of a Generalized (1 + 1) Dimensional System of Equations via Symbolic Computation
title_sort	exact solutions and conservation laws of a generalized (1 + 1) dimensional system of equations via symbolic computation
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/f2647f026b4240b09883932b02499085
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Exact Solutions and Conservation Laws of a Generalized (1 + 1) Dimensional System of Equations via Symbolic Computation

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