Symmetries of partial differential equations

Hervé Gaussier (1) , Joel Merker (1)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités

We establish a link between the study of completely integrable systems of partial differential equations and the study of generic submanifolds in C^n. 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.

Domaines: Géométrie différentielle [math.DG]

Hervé Gaussier, Joel Merker. Symmetries of partial differential equations. Journal of the Korean Mathematical Society, 2003, 40, pp.no. 3, 517-561. ⟨hal-00003404⟩