On the contact linearization of Monge–Ampere equations

This paper is devoted to the solution of a number of problems related to the contact classification of Monge–Ampere equations with two independent variables. In the 1870s Sophus Lie formulated the problem of finding whether a local reduction of a given Monge–Ampere equation to some simpler second-order equation (to a semilinear, linear with respect to the derivatives, equation with constant coefficients) is possible. In this paper conditions are studied that yield a realization of such a reduction. As objects that occur in the formulation of these conditions, we use the characteristic bundles of the given Monge–Ampere equation and their derivatives.