{
  "abstract": "We prove action and spectral stability near finite-gap tori of the periodic Korteweg--de Vries equation under autonomous analytic Hamiltonian perturbations of size $\\varepsilon$. The estimates are uniform over prescribed compact families, without small-amplitude or nonresonance assumptions, and allow nearby initial data with infinitely many open gaps. Assuming a strong solution and a uniform higher Sobolev bound on $[0,T_0/\\varepsilon]$, we permit one-derivative loss in the perturbing Hamiltonian's normal gradient. For sufficiently small $\\varepsilon$ and initial normal Birkhoff size $r_0$, the tangential action variations and weighted sum of normal actions are bounded by $C_δ(r_0^2+\\varepsilon^{2δ})$, while the spectral-gap variation in $\\ell^2$ is bounded by $C_δ(r_0+\\varepsilon^δ)$, for every $0<δ<1/4$. A key ingredient is coercivity of the negative Hessian of the nonlinear KdV Hamiltonian on the full $\\ell^2$ action space at every finite-gap action. We combine this with resonance analysis and corrected action observables evaluated along the solution. The hypotheses are verified for several local and nonlocal Hamiltonian perturbations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34601",
  "author_total": 1,
  "authors": [
    {
      "name": "Guan Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/23s6hkewdsd07.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34601",
  "fulltext_url": null,
  "id": "23s6hkewdsd07",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34601",
  "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"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7224016006",
  "pdf_url": "https://arxiv.org/pdf/2610.34601",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/23s6hkewdsd07.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34601",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34601"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Long-time action stability for perturbed KdV near finite-gap tori",
  "title_text": "Long-time action stability for perturbed KdV near finite-gap tori",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/23s6hkewdsd07",
  "venue": "arXiv",
  "versions": []
}