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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| Дата: | 2013 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2013
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.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| id |
irk-123456789-149204 |
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dspace |
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irk-123456789-1492042019-02-20T01:24:46Z Multi-Component Integrable Systems and Invariant Curve Flows in Certain Geometries Qu, C. Song, J. Yao, R. 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. 2013 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/149204 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Qu, C. Song, J. Yao, R. |
| spellingShingle |
Qu, C. Song, J. Yao, R. Multi-Component Integrable Systems and Invariant Curve Flows in Certain Geometries Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Qu, C. Song, J. Yao, R. |
| author_sort |
Qu, C. |
| title |
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_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_sort |
multi-component integrable systems and invariant curve flows in certain geometries |
| publisher |
Інститут математики НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149204 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT quc multicomponentintegrablesystemsandinvariantcurveflowsincertaingeometries AT songj multicomponentintegrablesystemsandinvariantcurveflowsincertaingeometries AT yaor multicomponentintegrablesystemsandinvariantcurveflowsincertaingeometries |
| first_indexed |
2023-05-20T17:31:42Z |
| last_indexed |
2023-05-20T17:31:42Z |
| _version_ |
1796153505381089280 |