A transformation of PDE systems related to the Drach theorem

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Abstract

We will define a new transformation of PDE systems as follows. Given a particular PDE system F, there is a new system F̂ whose solutions are the spaces of elements attached to the solutions of F. We will show that the system F̂ is a second order PDE system in a single unknown. As an application, we will derive as well a global version of the Drach theorem.

Keywords

PDE systems
Transformation
Contact element
Jet
Symplectic manifold
Lagrangian submanifold

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The author was partially founded by Junta de Castilla y León under contract SA077/03.