{
  "id": "2505.06220",
  "version": "v1",
  "published": "2025-05-09T17:55:55.000Z",
  "updated": "2025-05-09T17:55:55.000Z",
  "title": "Hamiltonian formalism for non-diagonalisable systems of hydrodynamic type",
  "authors": [
    "Paolo Lorenzoni",
    "Sara Perletti",
    "Karoline van Gemst"
  ],
  "comment": "43 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-09T17:55:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hydrodynamic type",
      "hamiltonian formalism",
      "non-diagonalisable systems",
      "generalises tsarevs integrable diagonal systems",
      "integrability conditions ensure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}