Hamiltonian structure of the complex Monge-Amp\`ere equation

TL;DR

This paper reveals the Hamiltonian structure of the complex Monge-Ampère equation in a first-order form, providing Lagrangian and Hamiltonian functions, a symplectic form, and a Hamiltonian operator for the Poisson bracket.

Contribution

It introduces the Hamiltonian formulation of the complex Monge-Ampère equation, including explicit structures like Lagrangian, Hamiltonian functions, and symplectic form.

Findings

Hamiltonian structure of the complex Monge-Ampère equation identified

Lagrangian and Hamiltonian functions constructed

Symplectic form and Hamiltonian operator derived

Abstract

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.