{
  "abstract": "We study the nonlinear Hamilton--Jacobi system arising as the formal semi-classical limit of the chordal Belavin--Polyakov--Zamolodchikov equations with a common eigenvalue parameter $λ$. We determine the number of global real-valued solutions modulo additive constants. When $λ=0$, the number of solutions can be derived using the connection between the solutions and rational functions, due to Eremenko. We focus on the case when $λ\\neq 0$ in this article. For $λ>0$, a Schwarzian correspondence relates the algebraic equations for the gradients to quasi-exponentials with prescribed critical points. Enumeration and transversality results of Mukhin, Tarasov, and Varchenko yield smooth real branches, and a Poisson bracket identity establishes their exactness. An energy bound rules out global real-valued solutions for $λ<0$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38192",
  "author_total": 2,
  "authors": [
    {
      "name": "Mo Chen"
    },
    {
      "name": "Hao Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/75aaey5vkqxt6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38192",
  "fulltext_url": null,
  "id": "75aaey5vkqxt6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38192",
  "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"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "3109|Nonlinear Waves and Solitons"
    ]
  ],
  "openalex": "W7215123851",
  "pdf_url": "https://arxiv.org/pdf/2609.38192",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/75aaey5vkqxt6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:22Z",
      "native_id": "2609.38192",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38192"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Quasi-exponentials and semi-classical limits for the chordal BPZ system",
  "title_text": "Quasi-exponentials and semi-classical limits for the chordal BPZ system",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/75aaey5vkqxt6",
  "venue": "arXiv",
  "versions": []
}