Backlund transformations for the sl(2) Gaudin magnet
  Elementary, one- and two-point, Backlund transformations are constructed for the generic case of the sl(2) Gaudin magnet. The spectrality property is used to construct these explicitly given, Poisson integrable maps which are time-discretizations of the continuous flows with any Hamiltonian from the spectral curve of the 2x2 Lax matrix. 
A.N.W. Hone, V.B. Kuznetsov and O. Ragnisco