Contact mappings of jet spaces

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 under which these mappings transform solutions of some partial differential equations into solutions 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.