Given an exterior differential system defined on a manifold M, the Cartan-Kuranishi prolongation theorem says that after a finite number of prolongations the system is either in involution (admits at least one 'large' integral manifold), or is impossible.

Reference

• M. Kuranishi, On É. Cartan's prolongation theorem of exterior differential systems, Amer. J. Math., vol. 79, 1957, p. 1-47

Partial differential equations | Mathematical theorems