Scalar differential invariants of symplectic Monge–Ampère equations

All second order scalar differential invariants of symplectic hyperbolic and elliptic Monge-Ampère PDEs with respect to symplectomorphisms are explicitly computed. In particular, it is shown that the number of independent second order invariants is equal to 7, in sharp contrast with general Monge-Ampère equations for which this number is equal to 2. A series of invariant differential forms and vector fields are also introduced: they allow one to construct numerous scalar differential invariants of higher order. The introduced invariants give a solution to the symplectic equivalence problem for Monge-Ampère equations.