Cover Image

The application of dressing method on nonlinear evolution equations

It is well known that Korteweg-de Vries (KdV) equation can be solved by inverse scattering transform (IST). Numerous efforts have been made to extend the range of application of this method. The question now is how wide is the class of equations which are integrable by IST? It would be more useful i...

Full description

Saved in:
Bibliographic Details
Main Author: Goh, Bor Chyuan
Format: Thesis
Language:English
Published: 2010
Subjects:
QA Mathematics
Online Access:http://eprints.utm.my/id/eprint/11298/4/GohBorChyuanMFS2010.pdf
http://eprints.utm.my/id/eprint/11298/
Tags: Add Tag
No Tags, Be the first to tag this record!
id my.utm.11298
record_format eprints
spelling my.utm.112982017-09-27T04:09:23Z http://eprints.utm.my/id/eprint/11298/ The application of dressing method on nonlinear evolution equations Goh, Bor Chyuan QA Mathematics It is well known that Korteweg-de Vries (KdV) equation can be solved by inverse scattering transform (IST). Numerous efforts have been made to extend the range of application of this method. The question now is how wide is the class of equations which are integrable by IST? It would be more useful if it could be extended or generalised to accommodate other equation. That's why we introduced dressing method which was proposed by Zakharov and Shabat (1974). The aim of dressing method is to generate integrable nonlinear equation and simultaneously its solution. We study this method on three integral operators and the differential operators. Besides that, we also study and list down all the properties which will be use together with operators in this method. In this dissertation, we choose only constant coefficient operator and scalar differential operator. We applied it to derive integrable nonlinear KdV and Kadomtsev-Petviashvili (KP) and thereafter we solve for exact solution. 2010-04 Thesis NonPeerReviewed application/pdf en http://eprints.utm.my/id/eprint/11298/4/GohBorChyuanMFS2010.pdf Goh, Bor Chyuan (2010) The application of dressing method on nonlinear evolution equations. Masters thesis, Universiti Teknologi Malaysia, Faculty of Science.
institution Universiti Teknologi Malaysia
building UTM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Malaysia
content_source UTM Institutional Repository
url_provider http://eprints.utm.my/
language English
topic QA Mathematics
spellingShingle QA Mathematics
Goh, Bor Chyuan
The application of dressing method on nonlinear evolution equations
description It is well known that Korteweg-de Vries (KdV) equation can be solved by inverse scattering transform (IST). Numerous efforts have been made to extend the range of application of this method. The question now is how wide is the class of equations which are integrable by IST? It would be more useful if it could be extended or generalised to accommodate other equation. That's why we introduced dressing method which was proposed by Zakharov and Shabat (1974). The aim of dressing method is to generate integrable nonlinear equation and simultaneously its solution. We study this method on three integral operators and the differential operators. Besides that, we also study and list down all the properties which will be use together with operators in this method. In this dissertation, we choose only constant coefficient operator and scalar differential operator. We applied it to derive integrable nonlinear KdV and Kadomtsev-Petviashvili (KP) and thereafter we solve for exact solution.
format Thesis
author Goh, Bor Chyuan
author_facet Goh, Bor Chyuan
author_sort Goh, Bor Chyuan
title The application of dressing method on nonlinear evolution equations
title_short The application of dressing method on nonlinear evolution equations
title_full The application of dressing method on nonlinear evolution equations
title_fullStr The application of dressing method on nonlinear evolution equations
title_full_unstemmed The application of dressing method on nonlinear evolution equations
title_sort application of dressing method on nonlinear evolution equations
publishDate 2010
url http://eprints.utm.my/id/eprint/11298/4/GohBorChyuanMFS2010.pdf
http://eprints.utm.my/id/eprint/11298/
_version_ 1643645642556309504
score 13.211869

Similar Items