{
  "abstract": "We derive several integrable equations in $(2+1)$ dimensions from the anti-self-dual Yang--Mills (ASDYM) equations with gauge group $G=\\mathrm{GL}(2,\\mathbb C)$ by imposing a single one-dimensional constraint on the ASDYM matrices. The resulting systems include the $(2+1)$-dimensional nonlinear Schrödinger (NLS) equation, a $(2+1)$-dimensional generalized derivative NLS family encompassing the Gerdjikov--Ivanov, Chen--Lee--Liu, and Kaup--Newell equations, and the $(2+1)$-dimensional Heisenberg ferromagnetic (HF) equation. The $(1+1)$-dimensional Wadati--Konno--Ichikawa equation is also recovered through a reciprocal transformation of the HF equation. The nonlinear variables and the associated gauge transformations are expressed explicitly in terms of the entries of the ASDYM matrices. The same one-dimensional constraint is implemented in the Cauchy matrix framework, yielding explicit solutions of the reduced integrable equations. In this formulation, the ASD Yang--Mills Lagrangian density is expressed in terms of a $τ$-function; for suitable exponential data, this $τ$-function becomes a Grammian-type $τ$-function of the Kadomtsev--Petviashvili equaton. The studies are extended to $\\mathrm{GL}(M,\\mathbb C)$ at the matrix level.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22753",
  "author_total": 3,
  "authors": [
    {
      "name": "Shangshuai Li"
    },
    {
      "name": "Ken-ichi Maruno"
    },
    {
      "name": "Da-jun Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dyc7acpnckx2n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22753",
  "fulltext_url": null,
  "id": "dyc7acpnckx2n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22753",
  "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",
      "nlin.SI"
    ],
    [
      "openalex",
      "3109|Nonlinear Waves and Solitons"
    ]
  ],
  "openalex": "W7222967736",
  "pdf_url": "https://arxiv.org/pdf/2610.22753",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dyc7acpnckx2n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:32Z",
      "native_id": "2610.22753",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22753"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:nlin.SI",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Realization of several related $(2+1)$-dimensional integrable systems via an anti-self-dual Yang--Mills reduction",
  "title_text": "Realization of several related (2+1)-dimensional integrable systems via an anti-self-dual Yang--Mills reduction",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:28Z",
  "url": "https://research.draconitic.com/paper/dyc7acpnckx2n",
  "venue": "arXiv",
  "versions": []
}