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Technical report: solutions of Korteweg-de Vries (KdV) equation / Faizatul Asyekin Yusri, Rusya Iryanti Yahaya and Nurhidayah Mat Ramli

In the present work, the derivation of Korteweg-de Vries (KdV) equation and its single­ soliton solution are shown step by step to give better understanding to people. This project is only devoted to shallow water waves where the derivation of KdV equation by using Euler equation in ( 1 + 1) dimensi...

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Main Authors: Yusri, Faizatul Asyekin, Yahaya, Rusya Iryanti, Mat Ramli, Nurhidayah
Format: Student Project
Language:English
Published: 2016
Subjects:
Study and teaching
Equations
Analysis
Online Access:https://ir.uitm.edu.my/id/eprint/109320/1/109320.pdf
https://ir.uitm.edu.my/id/eprint/109320/
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spelling my.uitm.ir.1093202025-02-03T16:30:50Z https://ir.uitm.edu.my/id/eprint/109320/ Technical report: solutions of Korteweg-de Vries (KdV) equation / Faizatul Asyekin Yusri, Rusya Iryanti Yahaya and Nurhidayah Mat Ramli Yusri, Faizatul Asyekin Yahaya, Rusya Iryanti Mat Ramli, Nurhidayah Study and teaching Equations Analysis In the present work, the derivation of Korteweg-de Vries (KdV) equation and its single­ soliton solution are shown step by step to give better understanding to people. This project is only devoted to shallow water waves where the derivation of KdV equation by using Euler equation in ( 1 + 1) dimensions is proposed. In the derivation, a set of governing equations is used and it follows the assumption of irrotational two-dimensional motion of an incompressible inviscid fluid that is bounded above by a free surface and below by a rigid horizontal plane. Then, scaling and substitution method are implemented. In addition, the far-field variables for wave that propagate to the right are also utilised. After solving the KdV equation, single-soliton solution for standard KdV equation is obtained from traveling wave solution which is one of the D' Alembert equation method. This project is then completed by sketching and plotting the graphs of solitons using Maple. These graphs illustrated the propagation of single-soliton solution to the right, left and both side of the graph. 2016 Student Project NonPeerReviewed text en https://ir.uitm.edu.my/id/eprint/109320/1/109320.pdf Technical report: solutions of Korteweg-de Vries (KdV) equation / Faizatul Asyekin Yusri, Rusya Iryanti Yahaya and Nurhidayah Mat Ramli. (2016) [Student Project] <http://terminalib.uitm.edu.my/109320.pdf> (Unpublished)
institution Universiti Teknologi Mara
building Tun Abdul Razak Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Mara
content_source UiTM Institutional Repository
url_provider http://ir.uitm.edu.my/
language English
topic Study and teaching
Equations
Analysis
spellingShingle Study and teaching
Equations
Analysis
Yusri, Faizatul Asyekin
Yahaya, Rusya Iryanti
Mat Ramli, Nurhidayah
Technical report: solutions of Korteweg-de Vries (KdV) equation / Faizatul Asyekin Yusri, Rusya Iryanti Yahaya and Nurhidayah Mat Ramli
description In the present work, the derivation of Korteweg-de Vries (KdV) equation and its single­ soliton solution are shown step by step to give better understanding to people. This project is only devoted to shallow water waves where the derivation of KdV equation by using Euler equation in ( 1 + 1) dimensions is proposed. In the derivation, a set of governing equations is used and it follows the assumption of irrotational two-dimensional motion of an incompressible inviscid fluid that is bounded above by a free surface and below by a rigid horizontal plane. Then, scaling and substitution method are implemented. In addition, the far-field variables for wave that propagate to the right are also utilised. After solving the KdV equation, single-soliton solution for standard KdV equation is obtained from traveling wave solution which is one of the D' Alembert equation method. This project is then completed by sketching and plotting the graphs of solitons using Maple. These graphs illustrated the propagation of single-soliton solution to the right, left and both side of the graph.
format Student Project
author Yusri, Faizatul Asyekin
Yahaya, Rusya Iryanti
Mat Ramli, Nurhidayah
author_facet Yusri, Faizatul Asyekin
Yahaya, Rusya Iryanti
Mat Ramli, Nurhidayah
author_sort Yusri, Faizatul Asyekin
title Technical report: solutions of Korteweg-de Vries (KdV) equation / Faizatul Asyekin Yusri, Rusya Iryanti Yahaya and Nurhidayah Mat Ramli
title_short Technical report: solutions of Korteweg-de Vries (KdV) equation / Faizatul Asyekin Yusri, Rusya Iryanti Yahaya and Nurhidayah Mat Ramli
title_full Technical report: solutions of Korteweg-de Vries (KdV) equation / Faizatul Asyekin Yusri, Rusya Iryanti Yahaya and Nurhidayah Mat Ramli
title_fullStr Technical report: solutions of Korteweg-de Vries (KdV) equation / Faizatul Asyekin Yusri, Rusya Iryanti Yahaya and Nurhidayah Mat Ramli
title_full_unstemmed Technical report: solutions of Korteweg-de Vries (KdV) equation / Faizatul Asyekin Yusri, Rusya Iryanti Yahaya and Nurhidayah Mat Ramli
title_sort technical report: solutions of korteweg-de vries (kdv) equation / faizatul asyekin yusri, rusya iryanti yahaya and nurhidayah mat ramli
publishDate 2016
url https://ir.uitm.edu.my/id/eprint/109320/1/109320.pdf
https://ir.uitm.edu.my/id/eprint/109320/
_version_ 1823097896473460736
score 13.239859

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