{
  "abstract": "This paper investigates the persistence of spatial analyticity for solutions to the dispersion-generalized periodic Korteweg-de Vries equation $$\\partial_tu-\\partial_x|D_x|^αu+u\\partial_xu=0,\\qquadα\\ge2.$$ For real-valued initial data $u_0\\in G^{σ_0,s}(\\mathbb T)$, with $σ_0>0$ and $s\\ge-α/4$, we prove that the corresponding global solution satisfies $$u\\in C([-T,T];G^{σ(T),s}(\\mathbb T)),\\qquadσ(T)=\\min\\left\\{σ_0,\\frac cT\\right\\},$$ for every $T>0$. As a consequence, our result improves the lower bound for the radius of spatial analyticity established by Himonas, Kalisch, and Selberg (2017) for $2\\leα<4$, including the classical periodic KdV equation, and establishes a unified $T^{-1}$ lower bound for the analyticity radius for every $α\\ge2$. The main novelties are twofold. First, we introduce a normal form reduction at the level of the Gevrey energy, which reveals an additional cancellation in the cubic Gevrey commutator and separates it into a non-accumulating boundary correction and a quartic remainder. Second, we establish a global-in-time periodic $L_{t,x}^4$ estimate for the non-polynomial phase $k|k|^α$, valid for every real $α\\ge2$. Together, these ingredients yield a refined almost conservation law and the $T^{-1}$ lower bound for the radius of spatial analyticity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06313",
  "author_total": 2,
  "authors": [
    {
      "name": "Jaeseop Ahn"
    },
    {
      "name": "Chulkwang Kwak"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dgfsgsfgsecfj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06313",
  "fulltext_url": null,
  "id": "dgfsgsfgsecfj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06313",
  "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/2611.06313",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dgfsgsfgsecfj.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06313",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06313"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Normal form smoothing and spatial analyticity for the dispersion-generalized periodic KdV equation",
  "title_text": "Normal form smoothing and spatial analyticity for the dispersion-generalized periodic KdV equation",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/dgfsgsfgsecfj",
  "venue": "arXiv",
  "versions": []
}