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arXiv · 2604.12819

Generalised (bi-)Hamiltonian structures of hydrodynamic type and (bi-)flat F-manifolds

Paolo Lorenzoni·Zhe Wang
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Abstract

We introduce the notions of generalised (bi-)Hamiltonian structures which generalise naturally the (bi-)Hamiltonian structures of evolutionary partial differential equations. In the hydrodynamic case, these structures are characterised in terms of geometric data. Furthermore, we show that a generalised (bi)-Hamiltonian structure of hydrodynamic type can be associated with any (bi-)flat F-manifold, and it is compatible with the corresponding principal hierarchy.

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Paolo Lorenzoni, Zhe Wang. 2026-04-14. Generalised (bi-)Hamiltonian structures of hydrodynamic type and (bi-)flat F-manifolds. https://arxiv.org/abs/2604.12819

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