{
  "abstract": "We study the quantised version of the Kadomtsev-Petviashvili equation in the formulation proposed in [4]. We analyse two aspects. One is the conservation of the first higher charge $H_3$ (besides the total mass $H_0$, the momentum $H_1$ and the Hamiltonian $H_2$). We find the expression of $H_3$ and prove commutativity, provided we regularise a specific ultraviolet divergence. The result then does not depend on the choice of a regulator, under fairly general assumptions. We then study the Bethe ansatz in finite volume and obtain a general solution to the two-body problem. We have used AI supervised by us to aid the proofs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15316",
  "author_total": 2,
  "authors": [
    {
      "name": "Chiara Paletta"
    },
    {
      "name": "Alessandro Torrielli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8mjc2r61z5mh8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15316",
  "fulltext_url": null,
  "id": "8mjc2r61z5mh8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15316",
  "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",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "nlin.SI"
    ],
    [
      "openalex",
      "3109|Nonlinear Waves and Solitons"
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  ],
  "openalex": "W7213348363",
  "pdf_url": "https://arxiv.org/pdf/2609.15316",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8mjc2r61z5mh8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.15316",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15316"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.SI",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "On the commuting charges and the Bethe ansatz for the quantised Kadomtsev-Petviashvili equation",
  "title_text": "On the commuting charges and the Bethe ansatz for the quantised Kadomtsev-Petviashvili equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/8mjc2r61z5mh8",
  "venue": "arXiv",
  "versions": []
}