Bäcklund Transformations for the Trigonometric Gaudin Magnet

Details Bäcklund Transformations for the Trigonometric Gaudin Magnet Bäcklund Transformations for the Trigonometric Gaudin Magnet

2009-12-12

arxiv.org/abs/0912.2456v2

SIGMA 6 (2010), 012, 6 pages

Nonlinear Sciences

Exactly Solvable and Integrable Systems

contribution to the Proc. of "Integrable Systems and Quantum Symmetries 2009", Prague, June 18-20, 2009

Scientific paper

10.3842/SIGMA.2010.012

We construct a Backlund 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.

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