Normal forms for parabolic Monge-Ampere equations

Ricardo Alonso Blanco; Gianni Manno; Fabrizio Pugliese

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arXiv · 0707.0683

Normal forms for parabolic Monge-Ampere equations

Ricardo Alonso Blanco·Gianni Manno·Fabrizio Pugliese

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Abstract

We find normal forms for parabolic Monge-Ampere 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-Ampere equations with symmetry properties, namely, the existence of classical or nonholonomic intermediate integrals. Our approach is based on the equivalence between parabolic Monge-Ampere 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 first order PDE's).

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Ricardo Alonso Blanco, Gianni Manno, Fabrizio Pugliese. 2007-09-15. Normal forms for parabolic Monge-Ampere equations. https://arxiv.org/abs/0707.0683

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