B\"acklund Transformations for the Trigonometric Gaudin Magnet
Orlando Ragnisco, Federico Zullo
TL;DR
This paper constructs a Backlund transformation for the trigonometric Gaudin magnet using Lax representation and spectrality, providing a new integrable transformation framework for this model.
Contribution
It introduces a novel Backlund transformation for the trigonometric Gaudin magnet based on Lax pairs and spectrality, expanding the tools for integrable systems analysis.
Findings
Constructed a Backlund transformation for the model
Derived a Darboux dressing matrix depending on one variable
Discussed open problems related to the transformation
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.
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