Homogeneous Hamiltonian operators and the theory of coverings

Pierandrea Vergallo; Raffaele Vitolo

Homogeneous Hamiltonian operators and the theory of coverings

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arxiv 2007.15294 v4 pith:3IB5LJIF submitted 2020-07-30 math-ph math.MPnlin.SI

Pierandrea Vergallo , Raffaele Vitolo This is my paper · ORCID

classification math-phmath.MPnlin.SI

keywords operatorsystemdifferentialpdesconservedcoveringshamiltonianhomogeneous

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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.

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