Symmetry condition in terms of Lie brackets

Abstract

A passive orthonomic system of PDEs defines a submanifold in the corresponding jet manifold, coordinated by so called parametric derivatives. We restrict the total differential operators and the prolongation of an evolutionary vector field v to this submanifold. We show that the vanishing of their commutators is equivalent to v being a generalized symmetry of the system.

10 pages, no figures, unpublished