Journal of the
Korean Mathematical Society JKMS

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

Keywords: Lie symmetry, completely integrable system, prologation, CR geometry, local holomorphic automorphism

MSC numbers: Primary 32V40, 34C14; Secondary 32V25, 32H02, 32H40, 32V10