Bäcklund Transformations for the Trigonometric Gaudin Magnet
arXiv:0912.2456 · doi:10.3842/SIGMA.2010.012
Abstract
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.
contribution to the Proc. of "Integrable Systems and Quantum Symmetries 2009", Prague, June 18-20, 2009