of the ordinary and partial differential equations that are regarded as being integrable or solvable may be obtained from the self-dual gauge field equations (or its generalizations) by reduction".
is the curvature of a connection on an oriented 4-dimensional pseudo-Riemannian manifold, and
They also obtain the equations of an integrable system known as the Euler–Arnold–Manakov top, a generalization of the Euler top, and they state that the Kovalevsaya top is also a reduction of the self-dual Yang–Mills equations.
Via the Penrose–Ward transform these solutions give the holomorphic vector bundles often seen in the context of algebraic integrable systems.
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