On the relation between standard and $μ$-symmetries for PDEs

Abstract

We give a geometrical interpretation of the notion of $μ$-prolongations of vector fields and of the related concept of $μ$-symmetry for partial differential equations (extending to PDEs the notion of $λ$-symmetry for ODEs). We give in particular a result concerning the relationship between $μ$-symmetries and standard exact symmetries. The notion is also extended to the case of conditional and partial symmetries, and we analyze the relation between local $μ$-symmetries and nonlocal standard symmetries.