Solving nonlinear Schrödinger equation of optical fiber type using inverse scattering transform
The main purpose of this study is to solve the nonlinear Schrödinger (NLS) equation of optical fiber type using inverse scattering transform (IST) method. Prior to that, simpler problem on the initial-valued Korteweg-de Vries (KdV) equation is discussed to show how such nonlinear evolution equation...
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my-utm-ep.1019372023-07-25T09:36:13Z Solving nonlinear Schrödinger equation of optical fiber type using inverse scattering transform 2020 Mohd. Yusof, Muhammad Fathullah QA Mathematics The main purpose of this study is to solve the nonlinear Schrödinger (NLS) equation of optical fiber type using inverse scattering transform (IST) method. Prior to that, simpler problem on the initial-valued Korteweg-de Vries (KdV) equation is discussed to show how such nonlinear evolution equation can be linearized and solved using IST. Then, a more general IST method based on two schemes known as AKNS (Ablowitz-Kaup-Newell-Sigur) and ZS (Zakharov-Shabat) are discussed. AKNS method is described in terms of scattering theory whereas ZS method is expressed solely based on operators. The NLS equation of optical fibre type should be solved using ZS scheme to avoid any specific calculations of the scattering data. Finally, the solutions obtained are used to demonstrate the occurence of solitons from the constructed graph using Mathematica software. It is found that the solution from the NLS equation is a propagating wave enveloped in a wave packet, called a bright soliton. On the other hand, the existence of dark soliton is also detected when the nonlinear term in the NLS equation is negative. Both of these solitons are able to retain its shape after moving over some distance on the graph. The occurence of solitons are able to be demonstrated based on the contructed graphs from the solutions of the NLS equation. 2020 Thesis http://eprints.utm.my/id/eprint/101937/ http://eprints.utm.my/id/eprint/101937/1/MuhammadFathullahMohdMFS2020.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:146266 masters Universiti Teknologi Malaysia, Faculty of Science Faculty of Science |
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Universiti Teknologi Malaysia |
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UTM Institutional Repository |
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English |
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QA Mathematics Mohd. Yusof, Muhammad Fathullah Solving nonlinear Schrödinger equation of optical fiber type using inverse scattering transform |
description |
The main purpose of this study is to solve the nonlinear Schrödinger (NLS) equation of optical fiber type using inverse scattering transform (IST) method. Prior to that, simpler problem on the initial-valued Korteweg-de Vries (KdV) equation is discussed to show how such nonlinear evolution equation can be linearized and solved using IST. Then, a more general IST method based on two schemes known as AKNS (Ablowitz-Kaup-Newell-Sigur) and ZS (Zakharov-Shabat) are discussed. AKNS method is described in terms of scattering theory whereas ZS method is expressed solely based on operators. The NLS equation of optical fibre type should be solved using ZS scheme to avoid any specific calculations of the scattering data. Finally, the solutions obtained are used to demonstrate the occurence of solitons from the constructed graph using Mathematica software. It is found that the solution from the NLS equation is a propagating wave enveloped in a wave packet, called a bright soliton. On the other hand, the existence of dark soliton is also detected when the nonlinear term in the NLS equation is negative. Both of these solitons are able to retain its shape after moving over some distance on the graph. The occurence of solitons are able to be demonstrated based on the contructed graphs from the solutions of the NLS equation. |
format |
Thesis |
qualification_level |
Master's degree |
author |
Mohd. Yusof, Muhammad Fathullah |
author_facet |
Mohd. Yusof, Muhammad Fathullah |
author_sort |
Mohd. Yusof, Muhammad Fathullah |
title |
Solving nonlinear Schrödinger equation of optical fiber type using inverse scattering transform |
title_short |
Solving nonlinear Schrödinger equation of optical fiber type using inverse scattering transform |
title_full |
Solving nonlinear Schrödinger equation of optical fiber type using inverse scattering transform |
title_fullStr |
Solving nonlinear Schrödinger equation of optical fiber type using inverse scattering transform |
title_full_unstemmed |
Solving nonlinear Schrödinger equation of optical fiber type using inverse scattering transform |
title_sort |
solving nonlinear schrödinger equation of optical fiber type using inverse scattering transform |
granting_institution |
Universiti Teknologi Malaysia, Faculty of Science |
granting_department |
Faculty of Science |
publishDate |
2020 |
url |
http://eprints.utm.my/id/eprint/101937/1/MuhammadFathullahMohdMFS2020.pdf |
_version_ |
1776100807532347392 |