{
  "abstract": "Following a recent characterisation of hydrodynamic systems with second-order Hamiltonian structure in terms of alternating three-forms on the projective space, we present a complete classification of systems in 6 components. We use non-trivial group action techniques to obtain 5 canonical forms. A general result for every dimension is also obtained for one of these cases, whose geometric structure is strictly related to the symplectic canonical form.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19785",
  "author_total": 3,
  "authors": [
    {
      "name": "Giorgio Gubbiotti"
    },
    {
      "name": "Lambertus Van Geemen"
    },
    {
      "name": "Pierandrea Vergallo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0eevf4c0ds3ef.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19785",
  "fulltext_url": null,
  "id": "0eevf4c0ds3ef",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19785",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.19785",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0eevf4c0ds3ef.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:19Z",
      "native_id": "2609.19785",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19785"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Classification of pairs of second-order Hamiltonian operators and hydrodynamic type systems in six components",
  "title_text": "Classification of pairs of second-order Hamiltonian operators and hydrodynamic type systems in six components",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/0eevf4c0ds3ef",
  "venue": "arXiv",
  "versions": []
}