Integrable equations of the dispersionless Hirota type

Let u(x, y, t) be a function of three variables x, y, t. Equations of the dispersionless Hirota type have the form: F(uxx, uxy, uyy, uxt, uyt, utt) = 0. Familiar examples include the Boyer–Finley equation Uxx + Uyy = eutt, the potential form of the dispersionless Kadomtsev–Petviashvili (dKP) equation Uxt - ½u²xx = uyy, the dispersionless Hirota equation (α - β)euxy + (β – γ)euyt + (γ – α)eutx = 0, etc. We study integrability of such systems in the sense of the existence of infinitely many hydrodynamic reductions. The moduli space of integrable equations of the dispersionless Hirota type is proved to be 21-dimensional. In addition, it is shown that the action of the equivalence group Sp(6) on the moduli space has an open orbit.