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

TL;DR

This paper develops a systematic method to discretize the rational su(2) Gaudin model, creating explicit integrable maps and discretizations that preserve the system's integrability, advancing the numerical analysis of such models.

Contribution

It introduces a novel integrable discretization of the rational su(2) Gaudin model using contraction procedures, linking continuous and discrete integrable systems.

Findings

Explicit integrable Poisson map for discretization

Constructed integrable discretizations of continuous systems

Established contraction procedures for system derivation

Abstract

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.