  A new method (by Kersten, Krasil'shchik and Verbovetsky), based on the theory
of differential coverings, allows to relate a system of PDEs with a
differential operator in such a way that the operator maps symmetries/conserved
quantities into symmetries/conserved quantities of the system of PDEs. When
applied to a quasilinear first-order system of PDEs and a Dubrovin-Novikov
homogeneous Hamiltonian operator the method yields conditions on the operator
and the system that have interesting differential and projective geometric
interpretations.
