Normal forms for parabolic Monge-Ampère equations
نویسنده
چکیده
We find normal forms for parabolic Monge-Ampère equations. Of these, the most general one holds for any equation admitting a complete integral. Moreover, we explicitly give the determining equation for such integrals; restricted to the analytic case, this equation is shown to have solutions. The other normal forms exhaust the different classes of parabolic Monge-Ampère equations with symmetry properties, namely, the existence of classical or nonholonomic intermediate integrals. Our approach is based on the equivalence between parabolic Monge-Ampère equations and particular distributions on a contact manifold, and involves a classification of vector fields lying in the contact structure. These are divided into three types and described in terms of the simplest ones (characteristic fields of 1 order PDE’s).
منابع مشابه
On normal forms for parabolic Monge-Ampère equations
Parabolic Monge-Ampère equations are divided into contact inequivalent classes, for each of which a normal form is given. Two of these are new in the C category.
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