Lie theorem via rank 2 distributions (integration of PDE of class ω=1)

2011/08/30 by Boris Kruglikov, Kruglikov, Boris · 1 citation
Mathematics · #Algebra over a field #Analysis of PDEs (math.AP) #Applied mathematics #Class (philosophy) #Combinatorics #Computer science #Differential Geometry (math.DG) #FOS: Mathematics #Fractional Differential Equations Solutions #Laplace transform #Mathematical analysis #Mathematical and Theoretical Analysis #Mathematics #Nonlinear system #Ode #Overdetermined system #Physics #Pure mathematics #Rank (graph theory) #math.AP #math.DG

paper · pdf · doi:10.48550/arxiv.1108.5854

arxiv created 2011/08/30 · openalex publication_date 2011/08/30 · arxiv updated 2011/08/31 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

In this paper we investigate compatible overdetermined systems of PDEs on the plane with one common characteristic. Lie's theorem states that its integration is equivalent to a system of ODEs, and we relate this to the geometry of rank 2 distributions. We find a criterion for integration in quadratures and in closed form, as in the method of Darboux, and discuss nonlinear Laplace transformations and symmetric PDE models.

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