Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 6 (2010), 012, 6 pages      arXiv:0912.2456
Contribution to the Proceedings of the XVIIIth International Colloquium on Integrable Systems and Quantum Symmetries

Bäcklund Transformations for the Trigonometric Gaudin Magnet

Orlando Ragnisco and Federico Zullo
Dipartimento di Fisica Universitá Roma Tre and Istituto Nazionale di Fisica Nucleare, Sezione di Roma, I-00146 Roma, Italy

Received December 12, 2009, in final form January 27, 2010; Published online January 29, 2010

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.

Key words: Bäcklund transformations; integrable maps; Gaudin systems.

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