{
  "abstract": "We discuss the existence of a well-defined $\\mathfrak{bms}_3$-integrable hierarchy, introduced in Fuentealba et al. (JHEP, 2018), using different structural methodologies. Specifically, from the variational complex on the ring of polynomial symbols, a $\\mathfrak{bms}_3$ bi-Hamiltonian structure is constructed on which a Nijenhuis operator can be attached. A similar argument is made for the $\\mathrm{AdS}_3$ case, where we check that the flat limit of the latter recovers the asymptotically flat situation. An alternative $τ$-scheme description is also presented. Moreover, a Lie-Poisson description suggests that such a $\\mathfrak{bms}_3$-hierarchy is not unique. For a subclass of so-called energy-dependent Schrödinger operators, it is shown that their Lax flows are described by the coadjoint orbits of $\\mathfrak{bms}_3$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.28454",
  "author_total": 1,
  "authors": [
    {
      "name": "Corentin Vitel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dkfv1ke9t2cpd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.28454",
  "fulltext_url": null,
  "id": "dkfv1ke9t2cpd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.28454",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "gr-qc"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "3109|Nonlinear Waves and Solitons"
    ]
  ],
  "openalex": "W7172008861",
  "pdf_url": "https://arxiv.org/pdf/2607.28454",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dkfv1ke9t2cpd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:37Z",
      "native_id": "2607.28454",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.28454"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Integrability in Asymptotic Symmetries of Spacetime: the $\\text{BMS}_3$ scenario",
  "title_text": "Integrability in Asymptotic Symmetries of Spacetime: the BMS_3 scenario",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/dkfv1ke9t2cpd",
  "venue": "arXiv",
  "versions": []
}