Admissible transformations and normalized classes of differential equations

Abstract:
The notion of a normalized class of differential equations is introduced. Roughly speaking, a class of differential equations is called normalized with respect to point transformations if any transformation that transforms a fixed equation from this class to an equation from the same class belongs to its equivalence group. Elementary properties of normalized classes, different kinds of normalization and using this notion in group classification problems are discussed. As a non-trivial example, hierarchy of normalized classes of nonlinear Schroedinger equations are investigated in detail.