Bäcklund Transformations for the Trigonometric Gaudin Magnet
We construct a Bäcklund transformation for the trigonometric classical Gaudin magnet starting from the Lax representation of the model. The Darboux dressing matrix obtained depends just on one set of variables because of the so-called spectrality property introduced by E. Sklyanin and V. Kuznetsov....
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2010 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2010
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146150 |
| 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: | Bäcklund Transformations for the Trigonometric Gaudin Magnet / O. Ragnisco, F. Zullo // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 13 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-146150 |
|---|---|
| record_format |
dspace |
| spelling |
Ragnisco, O. Zullo, F. 2019-02-07T19:06:51Z 2019-02-07T19:06:51Z 2010 Bäcklund Transformations for the Trigonometric Gaudin Magnet / O. Ragnisco, F. Zullo // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 13 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37J35; 70H06; 70H15 https://nasplib.isofts.kiev.ua/handle/123456789/146150 We construct a Bäcklund transformation for the trigonometric classical Gaudin magnet starting from the Lax representation of the model. The Darboux dressing matrix obtained depends just on one set of variables because of the so-called spectrality property introduced by E. Sklyanin and V. Kuznetsov. In the end we mention some possibly interesting open problems. This paper is a contribution to the Proceedings of the XVIIIth International Colloquium on Integrable Systems and Quantum Symmetries (June 18–20, 2009, Prague, Czech Republic). The full collection is available at http://www.emis.de/journals/SIGMA/ISQS2009.html. This paper is intended to be a contribution to the Proceedings of the International Conference “Integrable Systems and Quantum Symmetries 2009”, organized by Professor C. Burd´ık and held ˇ in Prague, June 18–20, 2009. One of the authors (O.R.) wants to warmly thank for his hospitality the Newton Institute for Mathematical Sciences, and all the organizers and the participants to the Program “Discrete Integrable Systems”. It was in fact during his stay in Cambridge that the main ideas presented in the paper have been made precise. Also, he acknowledges enlightening discussions with A. Levine (ITEF) at the workshop “Einstein at SISSA 2009”, partially funded by the Russian Foundation for Basic Research within the project “The Theory of Nonlinear Integrable Systems” en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Bäcklund Transformations for the Trigonometric Gaudin Magnet Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Bäcklund Transformations for the Trigonometric Gaudin Magnet |
| spellingShingle |
Bäcklund Transformations for the Trigonometric Gaudin Magnet Ragnisco, O. Zullo, F. |
| title_short |
Bäcklund Transformations for the Trigonometric Gaudin Magnet |
| title_full |
Bäcklund Transformations for the Trigonometric Gaudin Magnet |
| title_fullStr |
Bäcklund Transformations for the Trigonometric Gaudin Magnet |
| title_full_unstemmed |
Bäcklund Transformations for the Trigonometric Gaudin Magnet |
| title_sort |
bäcklund transformations for the trigonometric gaudin magnet |
| author |
Ragnisco, O. Zullo, F. |
| author_facet |
Ragnisco, O. Zullo, F. |
| publishDate |
2010 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We construct a Bäcklund transformation for the trigonometric classical Gaudin magnet starting from the Lax representation of the model. The Darboux dressing matrix obtained depends just on one set of variables because of the so-called spectrality property introduced by E. Sklyanin and V. Kuznetsov. In the end we mention some possibly interesting open problems.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146150 |
| citation_txt |
Bäcklund Transformations for the Trigonometric Gaudin Magnet / O. Ragnisco, F. Zullo // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 13 назв. — англ. |
| work_keys_str_mv |
AT ragniscoo backlundtransformationsforthetrigonometricgaudinmagnet AT zullof backlundtransformationsforthetrigonometricgaudinmagnet |
| first_indexed |
2025-12-07T15:31:11Z |
| last_indexed |
2025-12-07T15:31:11Z |
| _version_ |
1850864012084903936 |