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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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/736765 |
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| _version_ | 1832564194621259776 |
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| author | Weiguo Rui Yao Long |
| author_facet | Weiguo Rui Yao Long |
| author_sort | Weiguo Rui |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-5a0aba7d58c5423d95afb2255e9a08ae |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-5a0aba7d58c5423d95afb2255e9a08ae2025-02-03T01:11:31ZengWileyJournal 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 |
| 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 |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2012/736765 |
| work_keys_str_mv | AT weiguorui integralbifurcationmethodtogetherwithatranslationdilationtransformationforsolvinganintegrable2componentcamassaholmshallowwatersystem AT yaolong integralbifurcationmethodtogetherwithatranslationdilationtransformationforsolvinganintegrable2componentcamassaholmshallowwatersystem |