Generalised (bi-)Hamiltonian structures of hydrodynamic type and (bi-)flat F-manifolds
Mathematical Physics
2026-04-20 v2 Differential Geometry
math.MP
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.
Cite
@article{arxiv.2604.12819,
title = {Generalised (bi-)Hamiltonian structures of hydrodynamic type and (bi-)flat F-manifolds},
author = {Paolo Lorenzoni and Zhe Wang},
journal= {arXiv preprint arXiv:2604.12819},
year = {2026}
}