Hamiltonian structure of the complex Monge-Amp\`ere equation
  We discover Hamiltonian structure of the complex Monge-Amp`ere equation when written in a first order two-component form. We present Lagrangian and Hamiltonian functions, a symplectic form and the Hamiltonian operator that determines the Poisson bracket. 
Y. Nutku and M. B. Sheftel