{
  "abstract": "We prove nondegeneracy, modulo horizontal translation, of the normalized Sadovskii vortex patch. Building on the free-boundary and root-map framework developed by Huang and Tong, we first obtain a precise quantitative approximation of an exact Sadovskii profile, trapping its free boundary between two explicit barriers constructed around a rational approximation. This localization is then used to control the natural weighted quadratic form at the touching configuration. In the odd class, a ground-state identity shows that horizontal translation is the only zero mode. In the even class, dilation gives a negative direction, while a finite-rank comparison on a compact part of the boundary together with analytic contact-tail estimates yields a positive gap on a codimension-one subspace. Consequently, the Sadovskii dipole is locally rigid at the linearized level once translation is fixed. The computer-assisted part is confined to rigorous interval verification of a finite collection of explicit inequalities; the continuum, contact and operator reductions are proved analytically.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13362",
  "author_total": 3,
  "authors": [
    {
      "name": "M. del Pino"
    },
    {
      "name": "M. Musso"
    },
    {
      "name": "J. Wei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d0sp855jp0vh6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13362",
  "fulltext_url": null,
  "id": "d0sp855jp0vh6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13362",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7213356837",
  "pdf_url": "https://arxiv.org/pdf/2609.13362",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d0sp855jp0vh6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13362",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13362"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Nondegeneracy of the Sadovskii vortex",
  "title_text": "Nondegeneracy of the Sadovskii vortex",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/d0sp855jp0vh6",
  "venue": "arXiv",
  "versions": []
}