"Weak" symmetries and adapted variables for differential equations

It is shown that the introduction of suitable "symmetry-adapted" variables for the study of differential equations can be efficient and useful even if the problem does not admit symmetries. This method not only provides new solutions but also leads to the introduction of weaker notions of symmetry, and allows a natural classification of the possible types of symmetry, each of which is characterized by a specific form of the equation when written in the appropriate variables. Some simple examples are briefly proposed.