ABSTRACT
The theory of Lie-Bäcklund groups gives an algorithmic method for constructing all local symmetries of differential equations, i.e., formal groups generated by the canonical Lie-Bäcklund operators. Generally speaking a closed theory of nonlocal symmetries can be constructed by the introduction of functions of an infinite number of variables; however, here one loses the possibility of a constructive calculation of nonlocal symmetries. In a number of cases nonlocal symmetries may be easily obtained by a recursion operator. Thus, for the construction of nonlocal symmetries a basic problem is the proper choice of nonlocal variables. They are defined by integrable systems of differential equations that relate the nonlocal variables to the original differential variable u. The choice of these differential equations is made on the basis of some additional considerations. In the example just considered, such an additional consideration was the principle of recursive construction of the symmetry operators.
