Homogeneous Hamiltonian operators and the theory of coverings

Abstract

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.