Multi-Hamiltonian structure of Plebanski's second heavenly equation
  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. 
F. Neyzi, Y. Nutku and M. B. Sheftel