Contact linearization of nondegenerate equations

The present paper is devoted to the problem of transforming the classical Monge–Ampère equations to the linear equations by change of variables.
The class of Monge–Ampère equations is distinguished from the variety of second-order partial differential equations by the property that this class is closed under contact transformations. This fact was known already to Sophus Lie who studied the Monge–Ampère equations using methods of contact geometry. Therefore it is natural to consider the classification problems for the Monge–Ampère equations with respect to the pseudogroup of contact transformations.
In the present paper we give the complete solution to the problem of linearization of regular elliptic and hyperbolic Monge–Ampère equations with respect to contact transformations. In order to solve this problem, we construct invariants of the Monge–Ampère equations and the Laplace differential forms, which involve the classical Laplace invariants as coefficients.