By Magri's Theorem, Self-Dual Gravity is Completely Integrable
arXiv:nlin/0702055 · doi:10.3842/SIGMA.2007.034
Abstract
By Magri's theorem the bi-Hamiltonian structure of Plebanski's second heavenly equation proves that (anti)-self-dual gravity is a completely integrable system in four dimensions.
This is a contribution to the Proc. of workshop on Geometric Aspects of Integrable Systems (July 17-19, 2006; Coimbra, Portugal), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/