{
  "abstract": "We study quantitative stability for the fractional Schrödinger equation $(-Δ)^s u+u-|u|^αu=0$ near finite sums of widely separated positive ground states. For every $n\\ge1$, $0<s<1$, and Sobolev-subcritical exponent $α>0$, we estimate the $H^s$ distance to the family of such sums in terms of the $H^{-s}$ norm of the equation's residual. The optimal rate changes at $α=n/[2(n+2s)]$, with a logarithmic correction at the threshold. Above the threshold the rate is $t^{(n+2s)/(n+2s+1)}$; below it the exponent is $[(1+α)(n+2s)-n/2]/(n+2s+1)$. The proof combines uniform invertibility away from the translation modes with precise interaction estimates and a weighted correction of the approximate configuration. This correction resolves the translation interactions even when the nonlinearity has a small exponent. We also construct nonnegative configurations that attain these rates. The estimates quantify the effect of the algebraic decay of fractional ground states on stability.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11204",
  "author_total": 3,
  "authors": [
    {
      "name": "Hua Chen"
    },
    {
      "name": "Yun-Lu Fan"
    },
    {
      "name": "Xin Liao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2aba3tfe12dzd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11204",
  "fulltext_url": null,
  "id": "2aba3tfe12dzd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11204",
  "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",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7221141156",
  "pdf_url": "https://arxiv.org/pdf/2610.11204",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2aba3tfe12dzd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11204",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11204"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp stability near sums of ground states for fractional Schrödinger equations",
  "title_text": "Sharp stability near sums of ground states for fractional Schrödinger equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/2aba3tfe12dzd",
  "venue": "arXiv",
  "versions": []
}