{
  "abstract": "We prove that a class of nonlocal nonlinearities on periodic Sobolev spaces can be expressed as a trace of the unique mild solution to a local dispersive problem consisting of a system of forced Schrödinger equations. The proof is based on a reformulation of the nonlocal nonlinearities as the resonant orbit average of a real-analytic function under the unitary group generated by the free Schrödinger operator $\\mathrm{i} \\partial_x^2$. We illustrate our result by providing an equivalent local reformulation for a recently obtained nonlocal amplitude equation that formally captures the dynamics of parabolic systems close to a conserved Hopf instability.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05071",
  "author_total": 2,
  "authors": [
    {
      "name": "Bastian Hilder"
    },
    {
      "name": "Christian Kuehn"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9at7fgzdwdmbs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05071",
  "fulltext_url": null,
  "id": "9at7fgzdwdmbs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05071",
  "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",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7211873872",
  "pdf_url": "https://arxiv.org/pdf/2609.05071",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9at7fgzdwdmbs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.05071",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05071"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A dispersive extension result for a class of nonlocal nonlinearities",
  "title_text": "A dispersive extension result for a class of nonlocal nonlinearities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/9at7fgzdwdmbs",
  "venue": "arXiv",
  "versions": []
}