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: | |
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| Format: | Thesis |
| Language: | English |
| Published: |
2013
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| Subjects: | |
| Online Access: | http://eprints.utm.my/id/eprint/32320/1/NoorAslindaAliMFS2013.pdf |
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| Summary: | 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. |
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