Contact mappings of differential equations

Abstract

In this paper we consider mappings of jet spaces that preserve the module of canonical Pfaffian forms, but are not generally invertible. These mappings are called contact. A lemma on the prolongation of contact mappings is proved. Conditions are found for which mappings transform solutions of some partial differential equations into ones of other equations. Examples of contact mappings of differential equations are given. We consider contact mappings depending on a parameter and give example of differential equation invariant under the maps.