An integrable discretization of the rational su(2) Gaudin model and related systems

The first part of the present paper is devoted to a systematic construction of continuous-time finite-dimensional integrable systems arising from the rational su(2) Gaudin model through certain contraction procedures. In the second part, we derive an explicit integrable Poisson map discretizing a particular Hamiltonian flow of the rational su(2) Gaudin model. Then, the contraction procedures enable us to construct explicit integrable discretizations of the continuous systems derived in the first part of the paper.

💡 Research Summary

The paper is divided into two main parts, each addressing a different but related problem in the theory of integrable systems derived from the rational su(2) Gaudin model. In the first part the authors develop a systematic “contraction” procedure that reduces the original high‑dimensional Gaudin model, which is defined by a set of N distinct poles (z_i) and associated su(2) spin variables (\mathbf S_i), to a hierarchy of lower‑dimensional integrable systems. The contraction consists of bringing several poles together (e.g., (z_i = z + \epsilon \xi_i) with (\epsilon\to0)) while simultaneously rescaling the spin variables so that the Lax matrix \