{
  "abstract": "We prove global well-posedness of the one-dimensional defocusing cubic nonlinear Schrödinger equation in the modulation space $M^{\\infty,1}(\\mathbb{R})$. This space imposes no spatial decay and contains $C_b^2(\\mathbb{R})$ as well as all absolutely convergent sums of plane waves. The result applies to arbitrary data in this space, including large smooth quasiperiodic profiles and their localized perturbations. The proof constructs a nonnegative density satisfying a local conservation law from forward Weyl ratios, which are defined through half-line square-integrable solutions of the associated spectral problem. A suitable nonlinear combination of localized integrals of this density controls the modulation norm. Finally, choosing the spatial localization scale and NLS scaling in a coordinated way makes the accumulated boundary flux small enough to continue every mild solution globally.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29147",
  "author_total": 1,
  "authors": [
    {
      "name": "Friedrich Klaus"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0k8qpcjkx154j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29147",
  "fulltext_url": null,
  "id": "0k8qpcjkx154j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29147",
  "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": "W7214353149",
  "pdf_url": "https://arxiv.org/pdf/2609.29147",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0k8qpcjkx154j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2609.29147",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29147"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Global well-posedness of defocusing cubic NLS in $M^{\\infty,1}(\\mathbb{R})$",
  "title_text": "Global well-posedness of defocusing cubic NLS in M^∞,1(ℝ)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/0k8qpcjkx154j",
  "venue": "arXiv",
  "versions": []
}