Hamiltonian formalism for non-diagonalisable systems of hydrodynamic type
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918015289786368 |
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| author | Lorenzoni, Paolo Perletti, Sara van Gemst, Karoline |
| author_facet | Lorenzoni, Paolo Perletti, Sara van Gemst, Karoline |
| contents | We study the system of first order PDEs for pseudo-Riemannian metrics governing the Hamiltonian formalism for systems of hydrodynamic type. In the diagonal setting the integrability conditions ensure the compatibility of this system and, thanks to a classical theorem of Darboux, the existence of a family of solutions depending on functional parameters. In this paper we study the generalisation of this result to a class of non-diagonalisable systems of hydrodynamic type that naturally generalises Tsarev's integrable diagonal systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06220 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hamiltonian formalism for non-diagonalisable systems of hydrodynamic type Lorenzoni, Paolo Perletti, Sara van Gemst, Karoline Mathematical Physics We study the system of first order PDEs for pseudo-Riemannian metrics governing the Hamiltonian formalism for systems of hydrodynamic type. In the diagonal setting the integrability conditions ensure the compatibility of this system and, thanks to a classical theorem of Darboux, the existence of a family of solutions depending on functional parameters. In this paper we study the generalisation of this result to a class of non-diagonalisable systems of hydrodynamic type that naturally generalises Tsarev's integrable diagonal systems. |
| title | Hamiltonian formalism for non-diagonalisable systems of hydrodynamic type |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2505.06220 |