## ABSTRACT

The crucial idea used for introducing the notion of new type of symmetries, called later nonclassical symmetry, is to change the classical criteria of Lie symmetry by inserting into the criteria an additional equation, which en produced by the symmetry in question. Integration of the system of determining applicable (DEs) is the given difficult task for finding nonclassical symmetry of partial differential equation (PDE) in question. It was the main reason why a new type of non-Lie symmetry introduced in was forgotten for almost 20 years. There are several types of non-Lie symmetries at the present time and each of them can be called a nonclassical symmetry. The system of determining applicable (DEs) for finding the nonclassical symmetry becomes nonlinear. Integration of the system of DEs is the given difficult task for finding nonclassical symmetry of PDE in question.