{
  "abstract": "An explicit formula is presented for the $\\mathbf N$-soliton solution to the Kaup--Kupershmidt equation, for any positive integer $\\mathbf N,$ by using the input data set consisting of $\\mathbf N$ distinct positive $p_j$-values and $\\mathbf N$ arbitrarily chosen positive $c_j$-values. The formula is derived from the solution to the inverse scattering problem for a third-order linear operator in the reflectionless case with the $p_j$-values related to the bound-state poles of a transmission coefficient and the $c_j$-values related to the bound-state dependency constants. It is indicated how the formula is constructed from the solution to a Riemann--Hilbert problem and from the solution to a Marchenko integral equation used in the formulation of the aforementioned inverse scattering problem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05613",
  "author_total": 3,
  "authors": [
    {
      "name": "Tuncay Aktosun"
    },
    {
      "name": "Ramazan Ercan"
    },
    {
      "name": "Mehmet Unlu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/anxj36tzs7xp4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05613",
  "fulltext_url": null,
  "id": "anxj36tzs7xp4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05613",
  "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",
      "nlin.SI"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05613",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/anxj36tzs7xp4.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:20:56Z",
      "native_id": "2611.05613",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05613"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:nlin.SI",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "The \\texorpdfstring{$\\mathbf N$-soliton}{N-soliton} solution formula for the Kaup--Kupershmidt equation",
  "title_text": "The \\texorpdfstring{N-soliton}{N-soliton} solution formula for the Kaup--Kupershmidt equation",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:19Z",
  "url": "https://research.draconitic.com/paper/anxj36tzs7xp4",
  "venue": "arXiv",
  "versions": []
}