Department of Physics "E. Fermi'',

Universita degli Studi di Pisa,

Via Buonarroti 2, Ed. B-C, 56 127 Pisa, ITALY

E-mail: cicogna@df.unipi.it

**A discussion on some different notions of symmetry
in differential problems**

**Abstract:**

The introduction of "symmetry-adapted" variables for the study of differential
equations is considered. It is shown that the procedure can be efficient
and useful even if the problem does not admit symmetries: this method leads
indeed to a natural classification of the possible types of symmetry (exact,
partial, conditional in the standard sense or in a weaker one), each of
which being characterized by a specific form of the equation written in
the appropriate variables.