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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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Main Author: Mohd. Yusof, Muhammad Fathullah
Format: Thesis
Language:English
Published: 2020
Subjects:
QA Mathematics
Online Access:http://eprints.utm.my/id/eprint/101937/1/MuhammadFathullahMohdMFS2020.pdf
http://eprints.utm.my/id/eprint/101937/
http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:146266
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spelling my.utm.1019372023-07-25T09:36:13Z http://eprints.utm.my/id/eprint/101937/ Solving nonlinear Schrödinger equation of optical fiber type using inverse scattering transform 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 NonPeerReviewed application/pdf en http://eprints.utm.my/id/eprint/101937/1/MuhammadFathullahMohdMFS2020.pdf Mohd. Yusof, Muhammad Fathullah (2020) Solving nonlinear Schrödinger equation of optical fiber type using inverse scattering transform. Masters thesis, Universiti Teknologi Malaysia, Faculty of Science. http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:146266
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
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
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
publishDate 2020
url http://eprints.utm.my/id/eprint/101937/1/MuhammadFathullahMohdMFS2020.pdf
http://eprints.utm.my/id/eprint/101937/
http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:146266
_version_ 1772811132521676800
score 13.211869

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