Multi-Component Integrable Systems and Invariant Curve Flows in Certain Geometries
In this paper, multi-component generalizations to the Camassa-Holm equation, the modified Camassa-Holm equation with cubic nonlinearity are introduced. Geometric formulations to the dual version of the Schrödinger equation, the complex Camassa-Holm equation and the multi-component modified Camassa-H...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2013 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2013
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/149204 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Multi-Component Integrable Systems and Invariant Curve Flows in Certain Geometries / C. Qu, J. Song, R. Yao // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 60 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862674057897443328 |
|---|---|
| author | Qu, C. Song, J. Yao, R. |
| author_facet | Qu, C. Song, J. Yao, R. |
| citation_txt | Multi-Component Integrable Systems and Invariant Curve Flows in Certain Geometries / C. Qu, J. Song, R. Yao // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 60 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this paper, multi-component generalizations to the Camassa-Holm equation, the modified Camassa-Holm equation with cubic nonlinearity are introduced. Geometric formulations to the dual version of the Schrödinger equation, the complex Camassa-Holm equation and the multi-component modified Camassa-Holm equation are provided. It is shown that these equations arise from non-streching invariant curve flows respectively in the three-dimensional Euclidean geometry, the two-dimensional Möbius sphere and n-dimensional sphere Sn(1). Integrability to these systems is also studied.
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| first_indexed | 2025-12-07T15:39:54Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149204 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:39:54Z |
| publishDate | 2013 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Qu, C. Song, J. Yao, R. 2019-02-19T18:35:09Z 2019-02-19T18:35:09Z 2013 Multi-Component Integrable Systems and Invariant Curve Flows in Certain Geometries / C. Qu, J. Song, R. Yao // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 60 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37K10; 51M05; 51B10 DOI: http://dx.doi.org/10.3842/SIGMA.2013.001 https://nasplib.isofts.kiev.ua/handle/123456789/149204 In this paper, multi-component generalizations to the Camassa-Holm equation, the modified Camassa-Holm equation with cubic nonlinearity are introduced. Geometric formulations to the dual version of the Schrödinger equation, the complex Camassa-Holm equation and the multi-component modified Camassa-Holm equation are provided. It is shown that these equations arise from non-streching invariant curve flows respectively in the three-dimensional Euclidean geometry, the two-dimensional Möbius sphere and n-dimensional sphere Sn(1). Integrability to these systems is also studied. This paper is a contribution to the Special Issue “Symmetries of Dif ferential Equations: Frames, Invariants and Applications”. The full collection is available at http://www.emis.de/journals/SIGMA/SDE2012.html.
 The authors would like to thank the anonymous referees for constructive suggestions and comments. This work was supported by the China NSF for Distinguished Young Scholars under Grant 10925104 and the China NSF under Grants 11071278 and 60970054. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Multi-Component Integrable Systems and Invariant Curve Flows in Certain Geometries Article published earlier |
| spellingShingle | Multi-Component Integrable Systems and Invariant Curve Flows in Certain Geometries Qu, C. Song, J. Yao, R. |
| title | Multi-Component Integrable Systems and Invariant Curve Flows in Certain Geometries |
| title_full | Multi-Component Integrable Systems and Invariant Curve Flows in Certain Geometries |
| title_fullStr | Multi-Component Integrable Systems and Invariant Curve Flows in Certain Geometries |
| title_full_unstemmed | Multi-Component Integrable Systems and Invariant Curve Flows in Certain Geometries |
| title_short | Multi-Component Integrable Systems and Invariant Curve Flows in Certain Geometries |
| title_sort | multi-component integrable systems and invariant curve flows in certain geometries |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149204 |
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