Institute of Mathematics of NAS of Ukraine,

3 Tereshchenkivs'ka Str.,

01601 Kyiv,

UKRAINE

E-mail: rop@imath.kiev.ua

**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.