Geometric Realizations of Bi-Hamiltonian Completely Integrable Systems
In this paper we present an overview of the connection between completely integrable systems and the background geometry of the flow. This relation is better seen when using a group-based concept of moving frame introduced by Fels and Olver in [Acta Appl. Math. 51 (1998), 161-213; 55 (1999), 127-208...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2008 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2008
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149050 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Geometric Realizations of Bi-Hamiltonian Completely Integrable Systems / G.M. Beffa // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 51 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862654381376143360 |
|---|---|
| author | Beffa, G.M. |
| author_facet | Beffa, G.M. |
| citation_txt | Geometric Realizations of Bi-Hamiltonian Completely Integrable Systems / G.M. Beffa // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 51 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this paper we present an overview of the connection between completely integrable systems and the background geometry of the flow. This relation is better seen when using a group-based concept of moving frame introduced by Fels and Olver in [Acta Appl. Math. 51 (1998), 161-213; 55 (1999), 127-208]. The paper discusses the close connection between different types of geometries and the type of equations they realize. In particular, we describe the direct relation between symmetric spaces and equations of KdV-type, and the possible geometric origins of this connection.
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| first_indexed | 2025-12-01T23:49:58Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149050 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-01T23:49:58Z |
| publishDate | 2008 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Beffa, G.M. 2019-02-19T13:19:38Z 2019-02-19T13:19:38Z 2008 Geometric Realizations of Bi-Hamiltonian Completely Integrable Systems / G.M. Beffa // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 51 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 37K25; 53A55 https://nasplib.isofts.kiev.ua/handle/123456789/149050 In this paper we present an overview of the connection between completely integrable systems and the background geometry of the flow. This relation is better seen when using a group-based concept of moving frame introduced by Fels and Olver in [Acta Appl. Math. 51 (1998), 161-213; 55 (1999), 127-208]. The paper discusses the close connection between different types of geometries and the type of equations they realize. In particular, we describe the direct relation between symmetric spaces and equations of KdV-type, and the possible geometric origins of this connection. This paper is a contribution to the Proceedings of the Seventh International Conference “Symmetry in Nonlinear Mathematical Physics” (June 24–30, 2007, Kyiv, Ukraine). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Geometric Realizations of Bi-Hamiltonian Completely Integrable Systems Article published earlier |
| spellingShingle | Geometric Realizations of Bi-Hamiltonian Completely Integrable Systems Beffa, G.M. |
| title | Geometric Realizations of Bi-Hamiltonian Completely Integrable Systems |
| title_full | Geometric Realizations of Bi-Hamiltonian Completely Integrable Systems |
| title_fullStr | Geometric Realizations of Bi-Hamiltonian Completely Integrable Systems |
| title_full_unstemmed | Geometric Realizations of Bi-Hamiltonian Completely Integrable Systems |
| title_short | Geometric Realizations of Bi-Hamiltonian Completely Integrable Systems |
| title_sort | geometric realizations of bi-hamiltonian completely integrable systems |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149050 |
| work_keys_str_mv | AT beffagm geometricrealizationsofbihamiltoniancompletelyintegrablesystems |