Backlund transformations for the elliptic Gaudin model and a Clebsch system

Details Backlund transformations for the elliptic Gaudin model and a Clebsch system Backlund transformations for the elliptic Gaudin model and a Clebsch system

2011-01-25

arxiv.org/abs/1101.4853v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

18 pages; the following article has been submitted to J. Math. Phys. After it is published, it will be found at http://jmp.aip

Scientific paper

A two-parameters family of Backlund transformations for the classical elliptic Gaudin model is constructed. The maps are explicit, symplectic, preserve the same integrals as for the continuous flows and are a time discretization of each of these flows. The transformations can map real variables into real variables, sending physical solutions of the equations of motion into physical solutions. The starting point of the analysis is the integrability structure of the model. It is shown how the analogue transformations for the rational and trigonometric Gaudin model are a limiting case of this one. An application to a particular case of the Clebsch system is given.

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