Classification of Monge-Ampère equations with two variables
Volume 50 / 1999
Banach Center Publications 50 (1999), 179-194
DOI: 10.4064/-50-1-179-194
Abstract
This paper deals with the classification of hyperbolic Monge-Ampère equations on a two-dimensional manifold. We solve the local equivalence problem with respect to the contact transformation group assuming that the equation is of general position nondegenerate type. As an application we formulate a new method of finding symmetries. This together with previous author's results allows to state the solution of the classical S. Lie equivalence problem for the Monge-Ampère equations.