{
  "abstract": "We prove effective stability and matching logarithmic upper bounds for small solutions of Hamiltonian PDEs on the one-dimensional torus. An analytic coefficient-majorant calculus and an explicit normal-form iteration yield stability times with logarithms of order $L^{1+1/p}/(\\log L)^{1/p}$ for Gevrey weights and $L^{1+(q-1)/(pq+1)}$ for logarithmic ultra-differentiable weights, where $L=\\log(1/\\varepsilon)$ and $p\\geq1$ measures the order dependence of the small divisors. Even frequencies are organized into the exact blocks $\\{n,-n\\}$; elementary frequency gaps and constant weights on these blocks close the energy estimate. We verify the hypotheses for convolution NLS, fractional NLS with every fixed noninteger exponent $η>1/2$, and a beam equation with a metric parameter and a variational gradient nonlinearity. Two fixed analytic nonlocal Hamiltonian PDEs admit finite-support solutions whose first prescribed norm amplification occurs on the same logarithmic scales along sequences $\\varepsilon_n\\to0$. The common lower theorem applies to every sufficiently small datum of each admissible equation. Its combination with these examples establishes sharpness of both regularity-dependent scales under the same analytic and arithmetic hypotheses.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29307",
  "author_total": 2,
  "authors": [
    {
      "name": "Bingqi Yu"
    },
    {
      "name": "Yong Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dpvx6pcex1yh3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29307",
  "fulltext_url": null,
  "id": "dpvx6pcex1yh3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29307",
  "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",
      "math.AP"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7223211673",
  "pdf_url": "https://arxiv.org/pdf/2610.29307",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dpvx6pcex1yh3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29307",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29307"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Effective stability and sharp logarithmic time scales for Hamiltonian PDEs on the circle",
  "title_text": "Effective stability and sharp logarithmic time scales for Hamiltonian PDEs on the circle",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/dpvx6pcex1yh3",
  "venue": "arXiv",
  "versions": []
}