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 conserved quantities into symmetries 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.

中文翻译：

---

齐次哈密顿算子和覆盖理论

一种基于差分覆盖理论的新方法（由Kersten，Krasil'shchik和Verbovetsky撰写）允许将PDE系统与差分算子相关联，以使算子将守恒量映射为PDE系统的对称性。 。当应用于PDE的拟线性一阶系统和Dubrovin-Novikov齐次哈密顿算子时，该方法在算子和系统上产生具有有趣的微分和投影几何解释的条件。