{
  "abstract": "We prove that the Kirchhoff-Pohozaev equation on any compact connected Riemannian manifold without boundary admits a Lax pair $(L,B)$, where $L$ is a self-adjoint finite-rank perturbation of the Laplace-Beltrami operator and $B$ is a skew-adjoint operator of finite rank, both depending analytically on the phase space variables. We study the spectrum of $L$ using the perturbative determinant which is known to determine its spectrum and to admit a product representation similar to that of the generating function in KdV. We use this to show that the dynamics of the integrals of motion constructed in \\cite{BoitiManfrin2026,BHMP,campos} admits a Lax pair formulation with the same operator $L$ and to get a new proof of the involutivity of these integrals.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34522",
  "author_total": 4,
  "authors": [
    {
      "name": "Dario Bambusi"
    },
    {
      "name": "Emanuele Haus"
    },
    {
      "name": "Simone Marrocco"
    },
    {
      "name": "Michela Procesi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7w79aq3apmesr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34522",
  "fulltext_url": null,
  "id": "7w79aq3apmesr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34522",
  "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",
      "math.AP"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7223927494",
  "pdf_url": "https://arxiv.org/pdf/2610.34522",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7w79aq3apmesr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34522",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34522"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Lax Pair for the Kirchhoff-Pohozaev equation",
  "title_text": "Lax Pair for the Kirchhoff-Pohozaev equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/7w79aq3apmesr",
  "venue": "arXiv",
  "versions": []
}