Nonlocal symmetries. Heuristic approach

A constructive method for constructing nonlocal symmetries of differential equations based on the Lie—Bäcklund theory of groups is developed. The concept of quasilocal symmetries is introduced. With the help of this method nonlocal symmetries of differential equations of the type of nonlinear thermal conductivity and gas dynamics are studied.Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki, Noveishie Dostizheniya, Vol. 34, pp. 3–83, 1989.