Integrability of dispersionless Hirota type equations in 4D and the symplectic Monge-Ampere property

E. V. Ferapontov, B. Kruglikov, V. Novikov

We prove that integrability of a dispersionless Hirota type equation implies the symplectic Monge-Ampere property in any dimension $\ge 4$. In 4D this yields a complete classifica…