Numerical investigations of waves interactions from forced Korteweg de Vries equations

Soliton generated by the Korteweg de Vries (KdV) equation forms a group of solitons ladder. During full interaction of multi-soliton solutions, three types of peaks were obtained, namely single, flat and double peak. Soliton generated by the forced Korteweg de Vries (fKdV) equation forms uniform sol...

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Main Author:	Kee, Boon Hui
Format:	Thesis
Language:	English
Published:	2016
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/78116/1/KeeBoonHuiPFS2016.pdf
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spelling	my-utm-ep.781162018-07-25T08:06:28Z Numerical investigations of waves interactions from forced Korteweg de Vries equations 2016-03 Kee, Boon Hui QA Mathematics Soliton generated by the Korteweg de Vries (KdV) equation forms a group of solitons ladder. During full interaction of multi-soliton solutions, three types of peaks were obtained, namely single, flat and double peak. Soliton generated by the forced Korteweg de Vries (fKdV) equation forms uniform solitons trains with equal amplitude. Various aspects of solitons interactions of the fKdV equation for free surface flow over uneven bottom topography have been investigated. Fluid flowing over uneven bottom topography can support wave propagation that generates upstream and downstream nonlinear wavetrains. Such forced nonlinear solitary waves occur naturally in the shallow water near the coastal region. The fKdV equation models the above phenomena in many cases, such as in the transcritical, weakly nonlinear and weakly dispersive region. Numerical method which involves the pseudo-spectral method is used to solve the fKdV equation as it is difficult to obtain the solution analytically, due to the presence of the forcing term and the broken symmetry. A group of uniform solitons having the same amplitude and speed will not collide when the bump size and bump speed are constant. A wave profile with time-dependent transcritical velocity was investigated with a variation of Froude number. As the Froude number changes, two sets of solitary waves travelling upstream were discovered. A set of these solitary waves have nearly uniform amplitude, while another set comprises of solitary waves with variable amplitude, which forms a pairwise and two pairwise interactions pattern in the transcritical region. In the case of multiple bumps, upstream-advancing nonlinear solitary waves which may be generated continuously and interact with each other when the distance between bumps, width and height of bumps were varied. Interesting interaction patterns of the collision between uniform solitons will provide a better understanding of the forcing caused by multiple bumps on water flow at the uneven bottom topography of a shallow water in a rectangular channel. 2016-03 Thesis http://eprints.utm.my/id/eprint/78116/ http://eprints.utm.my/id/eprint/78116/1/KeeBoonHuiPFS2016.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:97209 phd doctoral Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Kee, Boon Hui Numerical investigations of waves interactions from forced Korteweg de Vries equations
description	Soliton generated by the Korteweg de Vries (KdV) equation forms a group of solitons ladder. During full interaction of multi-soliton solutions, three types of peaks were obtained, namely single, flat and double peak. Soliton generated by the forced Korteweg de Vries (fKdV) equation forms uniform solitons trains with equal amplitude. Various aspects of solitons interactions of the fKdV equation for free surface flow over uneven bottom topography have been investigated. Fluid flowing over uneven bottom topography can support wave propagation that generates upstream and downstream nonlinear wavetrains. Such forced nonlinear solitary waves occur naturally in the shallow water near the coastal region. The fKdV equation models the above phenomena in many cases, such as in the transcritical, weakly nonlinear and weakly dispersive region. Numerical method which involves the pseudo-spectral method is used to solve the fKdV equation as it is difficult to obtain the solution analytically, due to the presence of the forcing term and the broken symmetry. A group of uniform solitons having the same amplitude and speed will not collide when the bump size and bump speed are constant. A wave profile with time-dependent transcritical velocity was investigated with a variation of Froude number. As the Froude number changes, two sets of solitary waves travelling upstream were discovered. A set of these solitary waves have nearly uniform amplitude, while another set comprises of solitary waves with variable amplitude, which forms a pairwise and two pairwise interactions pattern in the transcritical region. In the case of multiple bumps, upstream-advancing nonlinear solitary waves which may be generated continuously and interact with each other when the distance between bumps, width and height of bumps were varied. Interesting interaction patterns of the collision between uniform solitons will provide a better understanding of the forcing caused by multiple bumps on water flow at the uneven bottom topography of a shallow water in a rectangular channel.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Kee, Boon Hui
author_facet	Kee, Boon Hui
author_sort	Kee, Boon Hui
title	Numerical investigations of waves interactions from forced Korteweg de Vries equations
title_short	Numerical investigations of waves interactions from forced Korteweg de Vries equations
title_full	Numerical investigations of waves interactions from forced Korteweg de Vries equations
title_fullStr	Numerical investigations of waves interactions from forced Korteweg de Vries equations
title_full_unstemmed	Numerical investigations of waves interactions from forced Korteweg de Vries equations
title_sort	numerical investigations of waves interactions from forced korteweg de vries equations
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2016
url	http://eprints.utm.my/id/eprint/78116/1/KeeBoonHuiPFS2016.pdf
_version_	1747817910902980608

Numerical investigations of waves interactions from forced Korteweg de Vries equations

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