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

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

2011-08-30

arxiv.org/abs/1108.5854v1

Mathematics

Analysis of PDEs

Scientific paper

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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