{
  "abstract": "In an earlier paper of P. Rossi and the first author, a construction of a wide class of quantum hierarchies was presented, with the input data given by an arbitrary cohomological field theory. A crucial role in the construction is played by the double ramification (DR) cycles on the moduli spaces of stable curves. As a special case, one gets a quantization of the hierarchy of the Intermediate Long Wave (ILW) equation. The ILW equation has two famous limits: the Korteweg--de Vries equation and the Benjamin--Ono (BO) equation, and for the latter one a quantum hierarchy was constructed by Nazarov and Sklyanin. In our paper, we propose a conjecture describing a relation between a limit of the quantum ILW hierarchy and the Nazarov--Sklyanin hierarchy and present various checks to support it.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01841",
  "author_total": 2,
  "authors": [
    {
      "name": "Alexandr Buryak"
    },
    {
      "name": "Abner Hernandez Rodriguez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6gz2k0tzeeynt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01841",
  "fulltext_url": null,
  "id": "6gz2k0tzeeynt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01841",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "nlin.SI"
    ],
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      "openalex",
      "3109|Nonlinear Waves and Solitons"
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  "openalex": "W7216380620",
  "pdf_url": "https://arxiv.org/pdf/2610.01841",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6gz2k0tzeeynt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2610.01841",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01841"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.SI",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Quantum hierarchies of the ILW and BO equations and the DR cycles on the moduli spaces of curves",
  "title_text": "Quantum hierarchies of the ILW and BO equations and the DR cycles on the moduli spaces of curves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/6gz2k0tzeeynt",
  "venue": "arXiv",
  "versions": []
}