Nonlinear evolutions equations in hirota's and sato's theories via young and maya diagrams

This work relates Hirota direct method to Sato theory. The bilinear direct method was introduced by Hirota to obtain exact solutions for nonlinear evolution equations. This method is applied to the Kadomtsev-Petviashvili (KP), KortewegdeVries (KdV), Sawada-Kotera (S-K) and sine-Gordon (s-G) equat...

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Main Author:	Ali, Noor Aslinda
Format:	Thesis
Language:	English
Published:	2013
Subjects:	Q Science (General)
Online Access:	http://eprints.utm.my/id/eprint/32320/1/NoorAslindaAliMFS2013.pdf
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spelling	my-utm-ep.323202017-07-31T08:05:11Z Nonlinear evolutions equations in hirota's and sato's theories via young and maya diagrams 2013 Ali, Noor Aslinda Q Science (General) This work relates Hirota direct method to Sato theory. The bilinear direct method was introduced by Hirota to obtain exact solutions for nonlinear evolution equations. This method is applied to the Kadomtsev-Petviashvili (KP), KortewegdeVries (KdV), Sawada-Kotera (S-K) and sine-Gordon (s-G) equations and solved to generate multi-soliton solutions. The Hirota’s scheme is shown to link to the Sato theory and later produced the Sato equation. It is also shown that the -function, which underlies the form of the soliton solutions, acts as the key function to express the solutions of the Sato equation. By using the results of group representation theory, particularly via Young and Maya diagrams, it is shown that the -function is naturally being governed by the class of physically significant nonlinear partial differential equations in the bilinear forms of Hirota scheme and are closely related to the Plucker relations. This framework is shown for Kadomtsev-Petviashvili (KP), KortewegdeVries (KdV), Sawada-Kotera (S-K) and sine-Gordon (s-G) equations. 2013 Thesis http://eprints.utm.my/id/eprint/32320/ http://eprints.utm.my/id/eprint/32320/1/NoorAslindaAliMFS2013.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:76591?queryType=vitalDismax&query=Nonlinear+evolutions+equations+in+hirota%27s+and+sato%27s+theories+via+young+and+maya+diagrams&public=true masters Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	Q Science (General)
spellingShingle	Q Science (General) Ali, Noor Aslinda Nonlinear evolutions equations in hirota's and sato's theories via young and maya diagrams
description	This work relates Hirota direct method to Sato theory. The bilinear direct method was introduced by Hirota to obtain exact solutions for nonlinear evolution equations. This method is applied to the Kadomtsev-Petviashvili (KP), KortewegdeVries (KdV), Sawada-Kotera (S-K) and sine-Gordon (s-G) equations and solved to generate multi-soliton solutions. The Hirota’s scheme is shown to link to the Sato theory and later produced the Sato equation. It is also shown that the -function, which underlies the form of the soliton solutions, acts as the key function to express the solutions of the Sato equation. By using the results of group representation theory, particularly via Young and Maya diagrams, it is shown that the -function is naturally being governed by the class of physically significant nonlinear partial differential equations in the bilinear forms of Hirota scheme and are closely related to the Plucker relations. This framework is shown for Kadomtsev-Petviashvili (KP), KortewegdeVries (KdV), Sawada-Kotera (S-K) and sine-Gordon (s-G) equations.
format	Thesis
qualification_level	Master's degree
author	Ali, Noor Aslinda
author_facet	Ali, Noor Aslinda
author_sort	Ali, Noor Aslinda
title	Nonlinear evolutions equations in hirota's and sato's theories via young and maya diagrams
title_short	Nonlinear evolutions equations in hirota's and sato's theories via young and maya diagrams
title_full	Nonlinear evolutions equations in hirota's and sato's theories via young and maya diagrams
title_fullStr	Nonlinear evolutions equations in hirota's and sato's theories via young and maya diagrams
title_full_unstemmed	Nonlinear evolutions equations in hirota's and sato's theories via young and maya diagrams
title_sort	nonlinear evolutions equations in hirota's and sato's theories via young and maya diagrams
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2013
url	http://eprints.utm.my/id/eprint/32320/1/NoorAslindaAliMFS2013.pdf
_version_	1747815974256508928

Nonlinear evolutions equations in hirota's and sato's theories via young and maya diagrams

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