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.