On decomposable Monge–Ampère equations

In this paper we introduce a remarkable class of Monge–Ampère systems on contact manifolds of arbitrary odd dimensions which we call decomposable Monge–Ampère systems. We show that we can associate to a decomposable Monge–Ampère system the characteristic systems enjoying nice properties, and that most of the results in the case of two independent variable as discussed in [M2] can be naturally generalized to this class of decomposable Monge–Ampère systems.