Integral Bifurcation Method together with a Translation-Dilation Transformation for Solving an Integrable 2-Component Camassa-Holm Shallow Water System

Integral Bifurcation Method together with a Translation-Dilation Transformation for Solving an Integrable 2-Component Camassa-Holm Shallow Water System

An integrable 2-component Camassa-Holm (2-CH) shallow water system is studied by using integral bifurcation method together with a translation-dilation transformation. Many traveling wave solutions of nonsingular type and singular type, such as solitary wave solutions, kink wave solutions, loop soli...

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Main Authors: Weiguo Rui, Yao Long
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/736765
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spelling doaj-5a0aba7d58c5423d95afb2255e9a08ae2020-11-24T20:59:06ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/736765736765Integral Bifurcation Method together with a Translation-Dilation Transformation for Solving an Integrable 2-Component Camassa-Holm Shallow Water SystemWeiguo Rui0Yao Long1Center for Nonlinear Science Research, College of Mathematics, Honghe University, Yunnan, Mengzi 661100, ChinaCenter for Nonlinear Science Research, College of Mathematics, Honghe University, Yunnan, Mengzi 661100, ChinaAn integrable 2-component Camassa-Holm (2-CH) shallow water system is studied by using integral bifurcation method together with a translation-dilation transformation. Many traveling wave solutions of nonsingular type and singular type, such as solitary wave solutions, kink wave solutions, loop soliton solutions, compacton solutions, smooth periodic wave solutions, periodic kink wave solution, singular wave solution, and singular periodic wave solution are obtained. Further more, their dynamic behaviors are investigated. It is found that the waveforms of some traveling wave solutions vary with the changes of parameter, that is to say, the dynamic behavior of these waves partly depends on the relation of the amplitude of wave and the level of water.http://dx.doi.org/10.1155/2012/736765
collection DOAJ
language English
format Article
sources DOAJ
author Weiguo Rui
Yao Long
spellingShingle Weiguo Rui
Yao Long
Integral Bifurcation Method together with a Translation-Dilation Transformation for Solving an Integrable 2-Component Camassa-Holm Shallow Water System
Journal of Applied Mathematics
author_facet Weiguo Rui
Yao Long
author_sort Weiguo Rui
title Integral Bifurcation Method together with a Translation-Dilation Transformation for Solving an Integrable 2-Component Camassa-Holm Shallow Water System
title_short Integral Bifurcation Method together with a Translation-Dilation Transformation for Solving an Integrable 2-Component Camassa-Holm Shallow Water System
title_full Integral Bifurcation Method together with a Translation-Dilation Transformation for Solving an Integrable 2-Component Camassa-Holm Shallow Water System
title_fullStr Integral Bifurcation Method together with a Translation-Dilation Transformation for Solving an Integrable 2-Component Camassa-Holm Shallow Water System
title_full_unstemmed Integral Bifurcation Method together with a Translation-Dilation Transformation for Solving an Integrable 2-Component Camassa-Holm Shallow Water System
title_sort integral bifurcation method together with a translation-dilation transformation for solving an integrable 2-component camassa-holm shallow water system
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2012-01-01
description An integrable 2-component Camassa-Holm (2-CH) shallow water system is studied by using integral bifurcation method together with a translation-dilation transformation. Many traveling wave solutions of nonsingular type and singular type, such as solitary wave solutions, kink wave solutions, loop soliton solutions, compacton solutions, smooth periodic wave solutions, periodic kink wave solution, singular wave solution, and singular periodic wave solution are obtained. Further more, their dynamic behaviors are investigated. It is found that the waveforms of some traveling wave solutions vary with the changes of parameter, that is to say, the dynamic behavior of these waves partly depends on the relation of the amplitude of wave and the level of water.
url http://dx.doi.org/10.1155/2012/736765
work_keys_str_mv AT weiguorui integralbifurcationmethodtogetherwithatranslationdilationtransformationforsolvinganintegrable2componentcamassaholmshallowwatersystem
AT yaolong integralbifurcationmethodtogetherwithatranslationdilationtransformationforsolvinganintegrable2componentcamassaholmshallowwatersystem
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