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.