{
  "abstract": "The scattering problem for the three-dimensional nonlinear Klein-Gordon equation \\begin{align*} u_{tt}-Δu+u=\\pm u^3 \\end{align*} is studied. It was shown that the scattering operator $\\mathbf{S}$ for the equation is well-defined on a neighborhood of 0 in the Sobolev space $\\mathcal{H}^{1/2}:=H^{1/2}(\\mathbb{R}^3) \\oplus H^{-1/2}(\\mathbb{R}^3)$, and that if $Φ_-$ is sufficiently small in $\\mathcal{H}^{1/2}$ and belongs to $\\mathcal{S} \\oplus \\mathcal{S}$, then $\\mathbf{S}Φ_-$ is also in $\\mathcal{S} \\oplus \\mathcal{S}$, where $\\mathcal{S}=\\mathcal{S}(\\mathbb{R}^3)$ is the Schwartz space. In the present paper, however, we prove that for any non-zero real-valued $Φ_-\\in\\mathcal{S}\\oplus\\mathcal{S}$ whose $\\mathcal{H}^{1/2}$-norm is sufficiently small, the corresponding solution $u$ satisfies \\[ U(-t) \\,{}^t(u(t),\\partial_t u(t)) \\not\\to \\mathbf{S}Φ_- \\quad(t\\to+\\infty) \\] in the weighted Sobolev space $H^{1,3}(\\mathbb{R}^3)\\oplus H^{0,3}(\\mathbb{R}^3)$ although $U(-t)\\,{}^t(u(t),\\partial_t u(t))$ converges to $\\mathbf{S}Φ_-$ in $H^{1,σ}(\\mathbb{R}^3)\\oplus H^{0,σ}(\\mathbb{R}^3)$ for any $σ<3$. Here, $U(t)$ denotes the free Klein-Gordon evolution group.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02707",
  "author_total": 1,
  "authors": [
    {
      "name": "Hironobu Sasaki"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4q64s78209hds.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02707",
  "fulltext_url": null,
  "id": "4q64s78209hds",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02707",
  "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/2611.02707",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4q64s78209hds.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02707",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02707"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Weighted Sobolev regularity and failure of profile convergence associated with the scattering operator for the three-dimensional cubic Klein-Gordon equation",
  "title_text": "Weighted Sobolev regularity and failure of profile convergence associated with the scattering operator for the three-dimensional cubic Klein-Gordon equation",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/4q64s78209hds",
  "venue": "arXiv",
  "versions": []
}