Transformation of hyperbolic Monge-Amp,re equations into linear equations with constant coefficients

A study was conducted to demonstrate the transformation of hyperbolic Monge-Ampére equations into linear equations with constant coefficients. The study demonstrated that the class of Monge-Ampére equations was closed under contact transformations, which is the property that differentiates the class from the entire set of second-order equations. It was also demonstrated that the Monge-Ampére equations can be characterized effectively in terms of differential forms on the 1-jet manifold. A number of effective forms were considered, to obtain aone-to-one map between the differential operators. A theorem was also proposed, under which the hyperbolic Monge-Ampére equation is locally contact equivalent to a linear equation with constant coefficients.