
Journal of Lie Theory 15 (2005), No. 1, 197218 Copyright Heldermann Verlag 2005 Correspondences between Jet Spaces and PDE Systems Sonia Jiménez Dept. of Mathematics, University of Salamanca, Plaza de la Merced 14, 37008 Salamanca, Spain sjv@usal.es Jesús Muñoz Dept. of Mathematics, University of Salamanca, Plaza de la Merced 14, 37008 Salamanca, Spain clint@usal.es Jesús Rodríguez Dept. of Mathematics, University of Salamanca, Plaza de la Merced 14, 37008 Salamanca, Spain jrl@usal.es Following some of Lie's ideas, we define between jet spaces canonical correspondences which allow us to associate with each first order PDE system another one with a single unknown function which contains as solutions that of the original system as well as its intermediate integrals. We also show for some systems of PDE that their integration is equivalent to that of their associated ones. Keywords: Jet, Lie correspondence, system of partial differential equations, involutive system, intermediate integral, Lie system. MSC: 58A20; 35A30 [ Fulltextpdf (257 KB)] for subscribers only. 