From su(2) Gaudin Models to Integrable Tops
In the present paper we derive two well-known integrable cases of rigid body dynamics (the Lagrange top and the Clebsch system) performing an algebraic contraction on the two-body Lax matrices governing the (classical) su(2) Gaudin models. The procedure preserves the linear r-matrix formulation of t...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2007 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2007
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147380 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | From su(2) Gaudin Models to Integrable Tops / M. Petrera, O. Ragnisco // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 29 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862742531542876160 |
|---|---|
| author | Petrera, M. Ragnisco, O. |
| author_facet | Petrera, M. Ragnisco, O. |
| citation_txt | From su(2) Gaudin Models to Integrable Tops / M. Petrera, O. Ragnisco // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 29 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In the present paper we derive two well-known integrable cases of rigid body dynamics (the Lagrange top and the Clebsch system) performing an algebraic contraction on the two-body Lax matrices governing the (classical) su(2) Gaudin models. The procedure preserves the linear r-matrix formulation of the ancestor models. We give the Lax representation of the resulting integrable systems in terms of su(2) Lax matrices with rational and elliptic dependencies on the spectral parameter. We finally give some results about the many-body extensions of the constructed systems.
|
| first_indexed | 2025-12-07T20:25:35Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147380 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T20:25:35Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Petrera, M. Ragnisco, O. 2019-02-14T14:54:25Z 2019-02-14T14:54:25Z 2007 From su(2) Gaudin Models to Integrable Tops / M. Petrera, O. Ragnisco // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 29 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 70E17; 70E40; 37J35 https://nasplib.isofts.kiev.ua/handle/123456789/147380 In the present paper we derive two well-known integrable cases of rigid body dynamics (the Lagrange top and the Clebsch system) performing an algebraic contraction on the two-body Lax matrices governing the (classical) su(2) Gaudin models. The procedure preserves the linear r-matrix formulation of the ancestor models. We give the Lax representation of the resulting integrable systems in terms of su(2) Lax matrices with rational and elliptic dependencies on the spectral parameter. We finally give some results about the many-body extensions of the constructed systems. This paper is a contribution to the Vadim Kuznetsov Memorial Issue ‘Integrable Systems and Related Topics’. M.P. thanks Yuri B. Suris and G. Satta for helpful comments. M.P. was partially supported by the European Community through the FP6 Marie Curie RTN ENIGMA (Contract number MRTN-CT-2004-5652) and by the European Science Foundation project MISGAM. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications From su(2) Gaudin Models to Integrable Tops Article published earlier |
| spellingShingle | From su(2) Gaudin Models to Integrable Tops Petrera, M. Ragnisco, O. |
| title | From su(2) Gaudin Models to Integrable Tops |
| title_full | From su(2) Gaudin Models to Integrable Tops |
| title_fullStr | From su(2) Gaudin Models to Integrable Tops |
| title_full_unstemmed | From su(2) Gaudin Models to Integrable Tops |
| title_short | From su(2) Gaudin Models to Integrable Tops |
| title_sort | from su(2) gaudin models to integrable tops |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147380 |
| work_keys_str_mv | AT petreram fromsu2gaudinmodelstointegrabletops AT ragniscoo fromsu2gaudinmodelstointegrabletops |