{
  "abstract": "We prove the soliton resolution conjecture for infinite-order multisoliton solutions in the sharp well-posedness space $H^s(\\mathbb R)$, $s>-\\frac12$, and construct soliton gases in $H^{s}(\\mathbb R)$ with arbitrary $s\\in\\mathbb R$, for the Benjamin--Ono equation. In particular, our work addresses two important open problems about inverse spectral for Lax operator, including the problem of spectral characterization of infinite-order multisolitons and that of determining the range of their asymptotic parameters. A central ingredient of our work is a spectral decomposition adapted to rough initial data. This extends the global soliton--radiation description to weakly weighted $H^s$ data while allowing infinite negative eigenvalues. Another important ingredient is a continuous norming action that extends finite inverse spectral shifts to gas limits while retaining a full continuous norming weight. Our framework provides a basis for studying infinite-order soliton resolution and the construction and asymptotics of soliton gases for nonlocal equations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38198",
  "author_total": 2,
  "authors": [
    {
      "name": "Hong-Yu Pan"
    },
    {
      "name": "Shou-Fu Tian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cg6359zq16m9v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38198",
  "fulltext_url": null,
  "id": "cg6359zq16m9v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38198",
  "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.AP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38198",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cg6359zq16m9v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38198",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38198"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Soliton resolution conjecture and soliton gases for the Benjamin-Ono equation with infinite-order multisolitons in the sharp well-posedness space",
  "title_text": "Soliton resolution conjecture and soliton gases for the Benjamin-Ono equation with infinite-order multisolitons in the sharp well-posedness space",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/cg6359zq16m9v",
  "venue": "arXiv",
  "versions": []
}