Multi-Hamiltonian structure of Plebanski's second heavenly equation
arXiv:nlin/0505030 · doi:10.1088/0305-4470/38/39/012
Abstract
We show that Plebanski's second heavenly equation, when written as a first-order nonlinear evolutionary system, admits multi-Hamiltonian structure. Therefore by Magri's theorem it is a completely integrable system. Thus it is an example of a completely integrable system in four dimensions.