Symmetries of partial differential equations

2004/04/13 by Hervé Gaussier, Joël Merker
Mathematics · #math.CV #math.DG #msc:32V40 #msc:34C14. #msc:32V25 #msc:32H02 #msc:32H40 #msc:32V10

paper · pdf

published as J. Korean Math. Soc. 40 (2003), no. 3, 517--561

arxiv created 2004/04/13 · arxiv updated 2009/12/01

Abstract

We establish a link between the study of completely integrable systems of partial differential equations and the study of generic submanifolds in Cⁿ. Using the recent developments of Cauchy-Riemann geometry we provide the set of symmetries of such a system with a Lie group structure. Finally we determine the precise upper bound of the dimension of this Lie group for some specific systems of partial differential equations.

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