The area of integrable systems lies at the boundary of mathematics and physics.
Integrable systems are universal limiting models of science that are widely applicable. The field grew from observations of astonishingly well-ordered and predictable behaviour in certain models of nonlinear lattices used to describe the thermal properties of metals and led to the theory of solitons and completely integrable systems, one of the most profound advances of twentieth century mathematics. Reductions led to the Painlevé equations, which are canonical representations of integrable models in one dimension.
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