ON THE DETERMINATION OF NONLOCAL SYMMETRIES

The importance of non-local symmetries of differential equations lies in their manifestation as Lie point symmetries of the equations result ing from reduction of order. The reason for the determination of these symmetries in second-order equations with only one Lie point symmetry is self-evident. However, the disadvantage of non-local symmetries is that no systematic approach to their determination exists. We present such an approach (applicable to differential equations of any order) and apply it to some second-order ordinary differential equations and show that they have a rich occurrence. We also look at possible genera lizations of the concept of non-local symmetries.