{
  "abstract": "We develop a generalized long-wave limit method for constructing higher-order (degenerate) lump solutions of $(2+1)$-dimensional integrable systems. Starting from the multi-soliton tau function, we introduce wavenumber rescalings, spectral perturbations, and higher-order phase modulations in a single small parameter, and choose their coefficients so that the lower-order Taylor coefficients vanish. Applying this framework to the Kadomtsev--Petviashvili I equation, we explicitly derive second-order two- and three-lump solutions as well as third-order three-, four-, five-, and six-lump solutions. The long-time asymptotics of the peak positions and amplitudes describe anomalous scattering of these degenerate lump solutions. Extensions to hybrid higher-order lump solutions associated with multiple distinct spectral parameters are also discussed.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.15174",
  "author_total": 2,
  "authors": [
    {
      "name": "Tianwei Qiu"
    },
    {
      "name": "Zhen Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/27frya365ec65.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.15174",
  "fulltext_url": null,
  "id": "27frya365ec65",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.15174",
  "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",
      "nlin.PS"
    ],
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      "arxiv",
      "nlin.SI"
    ],
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      "openalex",
      "3109|Nonlinear Waves and Solitons"
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  ],
  "openalex": "W7164890975",
  "pdf_url": "https://arxiv.org/pdf/2606.15174",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/27frya365ec65.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:32Z",
      "native_id": "2606.15174",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.15174"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.PS",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "A generalized long-wave limit method with spectral perturbations",
  "title_text": "A generalized long-wave limit method with spectral perturbations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/27frya365ec65",
  "venue": "arXiv",
  "versions": []
}