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Bäcklund Transformations for the Trigonometric Gaudin Magnet
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6
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- Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6, випуск за цей рік
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Bäcklund Transformations for the Trigonometric Gaudin Magnet
Інший ID:
2010 Mathematics Subject Classification: 37J35; 70H06; 70H15
Посилання:
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.
Підтримка:
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”
Дата:
2010
Переглядів:
751
Завантажень:
283
Анотація:
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.
