Garnier integrable system

In mathematical physics, the Garnier integrable system, also known as the classical Gaudin model is a classical mechanical system discovered by René Garnier in 1919 by taking the 'Painlevé simplification' or 'autonomous limit' of the Schlesinger equations. It is a classical analogue to the quantum Gaudin model due to Michel Gaudin (similarly, the Schlesinger equations are a classical analogue to the Knizhnik–Zamolodchikov equations). The classical Gaudin models are integrable.

They are also a specific case of Hitchin integrable systems, when the algebraic curve that the theory is defined on is the Riemann sphere and the system is tamely ramified.