Generalised (bi-)Hamiltonian structures of hydrodynamic type and (bi-)flat F-manifolds
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| Format: | Preprint |
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2026
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| _version_ | 1866910137975832576 |
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| author | Lorenzoni, Paolo Wang, Zhe |
| author_facet | Lorenzoni, Paolo Wang, Zhe |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_12819 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generalised (bi-)Hamiltonian structures of hydrodynamic type and (bi-)flat F-manifolds Lorenzoni, Paolo Wang, Zhe Mathematical Physics Differential Geometry 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. |
| title | Generalised (bi-)Hamiltonian structures of hydrodynamic type and (bi-)flat F-manifolds |
| topic | Mathematical Physics Differential Geometry |
| url | https://arxiv.org/abs/2604.12819 |