Note di Matematica 23

Giuseppe Gaeta, Paola Morando
2004 unpublished
So called λ-symmetries were introduced by Muriel and Romero, and geometrically characterized by Pucci and Saccomandi [8, 12], in the ODE case. We extend them to the PDE framework. In this context the central object is a horizontal one-form µ, and we speak of µ-prolongations of vector fields and µ-symmetries of PDEs. The latter are as good as standard symmetries in providing symmetry reduction of PDEs (or systems thereof) and explicit invariant solutions.