Existence and Construction of Vessiot Connections

Abstract

A rigorous formulation of Vessiot's vector field approach to the analysis of general systems of partial differential equations is provided. It is shown that this approach is equivalent to the formal theory of differential equations and that it can be carried through if, and only if, the given system is involutive. As a by-product, we provide a novel characterisation of transversal integral elements via the contact map.

Keywords

• formal integrability
• integral element
• involution
• partial differential equation
• Vessiot connection
• Vessiot distribution