PDEs reduction and -symmetries

Abstract

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 , and we speak of -prolongations of vector fields and -symmetries of PDEs.The latter are as good as standard symmetries in providing symmetry reduction of PDEs (or systems thereof) and explicit invariant solutions.