{
  "abstract": "We present a classification of supersymmetric bilinear KdV-type equations admitting unconstrained three-super-soliton solutions. Extending Hirota's classical three-soliton criterion to the supersymmetric setting, we derive the complete bosonic and fermionic compatibility conditions governing the existence of three-super-soliton solutions. We prove that every supersymmetric bilinear KdV-type equation possesses unconstrained one- and two-super-soliton solutions, whereas three-super-soliton solutions exist only when eight integrability conditions are satisfied. These conditions provide a supersymmetric analogue of Hirota's classical integrability criterion and naturally recover the fermionic relations previously introduced by Carstea, revealing their structural origin. As a consequence, we classify the supersymmetric extensions of Hirota bilinear KdV-type equations and show that only a subset of Hietarinta's classical classification remains valid in the unrestricted supersymmetric framework.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14372",
  "author_total": 2,
  "authors": [
    {
      "name": "Laurent Delisle"
    },
    {
      "name": "Amine Jaouadi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2nydxdcx8vdkm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14372",
  "fulltext_url": null,
  "id": "2nydxdcx8vdkm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14372",
  "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"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.14372",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2nydxdcx8vdkm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.14372",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14372"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.SI",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "A Classification of Hirota-Integrable Supersymmetric Bilinear KdV-Type Equations",
  "title_text": "A Classification of Hirota-Integrable Supersymmetric Bilinear KdV-Type Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:25Z",
  "url": "https://research.draconitic.com/paper/2nydxdcx8vdkm",
  "venue": "arXiv",
  "versions": []
}