{
  "abstract": "We develop a twisted Marchenko lemma with applications into non-commutative two-component integrable systems. Starting from a twisted differential equation, we introduce the corresponding two-component Wronski matrix $W_{n,m}(\\boldsymbolϕ,\\boldsymbolψ)$. Under the Marchenko lemma conditions, the logarithmic derivative $(\\partial W_{n,m})W_{n,m}^{-1}$ satisfies nonlinear equations, whose two-component projections yield a non-commutative two-component KP equation, while a single-component reduction recovers the non-commutative Burgers equation, KP equation and DS equation. A direct approach based on two-component quasi-Wronskians is developed, from which a higher-order non-commutative two-component KP equation is generated with matrix-valued solutions. Reductions of the seed functions of the non-commutative two-component KP hierarchy yield the one-component counterpart, while a stepwise reduction of those for the two-component KP equation gives the non-commutative DS and NLS equations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28233",
  "author_total": 3,
  "authors": [
    {
      "name": "Jun-Yang Zhang"
    },
    {
      "name": "Shi-Hao Li"
    },
    {
      "name": "Shou-Feng Shen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9ekcw6cpeq9gv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28233",
  "fulltext_url": null,
  "id": "9ekcw6cpeq9gv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28233",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "nlin.SI"
    ],
    [
      "openalex",
      "3109|Nonlinear Waves and Solitons"
    ]
  ],
  "openalex": "W7223121091",
  "pdf_url": "https://arxiv.org/pdf/2610.28233",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9ekcw6cpeq9gv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2610.28233",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28233"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.SI",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "A twisted Marchenko lemma and applications",
  "title_text": "A twisted Marchenko lemma and applications",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/9ekcw6cpeq9gv",
  "venue": "arXiv",
  "versions": []
}