This article is cited in 6 papers

Bäcklund Transformations for the Trigonometric Gaudin Magnet

Orlando Ragnisco, Federico Zullo

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

Abstract: 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.

Keywords: Bäcklund transformations; integrable maps; Gaudin systems.

MSC: 37J35; 70H06; 70H15

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

Language: English

DOI: 10.3842/SIGMA.2010.012

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ArXiv: 0912.2456