Symmetry and double reduction for exact solutions of selected nonlinear partial differential equations

Amongst the several analytic methods available to obtain exact solutions of non-linear differential equations, Lie symmetry reduction and double reduction technique are proven to be most effective and have attracted researcher from different areas to utilize these methods in their research. In this...

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Main Author:	Boon, Joseph Zik Hong
Format:	Thesis
Language:	English
Published:	2017
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/79334/1/BoonJosephZikHongPFS2017.pdf
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id	my-utm-ep.79334
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spelling	my-utm-ep.793342018-10-14T08:44:31Z Symmetry and double reduction for exact solutions of selected nonlinear partial differential equations 2017 Boon, Joseph Zik Hong QA Mathematics Amongst the several analytic methods available to obtain exact solutions of non-linear differential equations, Lie symmetry reduction and double reduction technique are proven to be most effective and have attracted researcher from different areas to utilize these methods in their research. In this research, Lie symmetry analysis and double reduction are used to find the exact solutions of nonlinear differential equations. For Lie symmetry reduction method, symmetries of differential equation will be obtained and hence invariants will be obtained, thus differential equation will be reduced and exact solutions are calculated. For the method of double reduction, we first find Lie symmetry, followed by conservation laws using ‘Multiplier’ approach. Finally, possibilities of associations between symmetry with conservation law will be used to reduce the differential equation, and thereby solve the differential equation. These methods will be used on some physically very important nonlinear differential equations; such as Kadomtsev- Petviashvili equation, Boyer-Finley equation, Short Pulse Equation, and Kortewegde Vries-Burgers equations. Furthermore, verification of the solution obtained also will be done by function of PDETest integrated in Maple or comparison to exist literature. 2017 Thesis http://eprints.utm.my/id/eprint/79334/ http://eprints.utm.my/id/eprint/79334/1/BoonJosephZikHongPFS2017.pdf application/pdf en public phd doctoral Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Boon, Joseph Zik Hong Symmetry and double reduction for exact solutions of selected nonlinear partial differential equations
description	Amongst the several analytic methods available to obtain exact solutions of non-linear differential equations, Lie symmetry reduction and double reduction technique are proven to be most effective and have attracted researcher from different areas to utilize these methods in their research. In this research, Lie symmetry analysis and double reduction are used to find the exact solutions of nonlinear differential equations. For Lie symmetry reduction method, symmetries of differential equation will be obtained and hence invariants will be obtained, thus differential equation will be reduced and exact solutions are calculated. For the method of double reduction, we first find Lie symmetry, followed by conservation laws using ‘Multiplier’ approach. Finally, possibilities of associations between symmetry with conservation law will be used to reduce the differential equation, and thereby solve the differential equation. These methods will be used on some physically very important nonlinear differential equations; such as Kadomtsev- Petviashvili equation, Boyer-Finley equation, Short Pulse Equation, and Kortewegde Vries-Burgers equations. Furthermore, verification of the solution obtained also will be done by function of PDETest integrated in Maple or comparison to exist literature.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Boon, Joseph Zik Hong
author_facet	Boon, Joseph Zik Hong
author_sort	Boon, Joseph Zik Hong
title	Symmetry and double reduction for exact solutions of selected nonlinear partial differential equations
title_short	Symmetry and double reduction for exact solutions of selected nonlinear partial differential equations
title_full	Symmetry and double reduction for exact solutions of selected nonlinear partial differential equations
title_fullStr	Symmetry and double reduction for exact solutions of selected nonlinear partial differential equations
title_full_unstemmed	Symmetry and double reduction for exact solutions of selected nonlinear partial differential equations
title_sort	symmetry and double reduction for exact solutions of selected nonlinear partial differential equations
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2017
url	http://eprints.utm.my/id/eprint/79334/1/BoonJosephZikHongPFS2017.pdf
_version_	1747818203106508800

Symmetry and double reduction for exact solutions of selected nonlinear partial differential equations

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