{
  "abstract": "We construct by convex integration a nonzero singular weak solution of the one-dimensional periodic cubic nonlinear Schrödinger equation that is compactly supported in time, has zero initial datum, and satisfies \\[ u\\in\\bigcap_{α<1/6} C_t^0 H_x^α\\cap \\bigcap_{1\\leq p<3} C_t^0 L_x^p. \\] The key new ingredient is a two-carrier perturbation: its zero-output interaction cancels the previous error, without introducing any zero Fourier mode, which is crucial in the cubic NLS. Whenever a singular solution belongs to \\(C_t^0L_x^3\\), this nonlinearity agrees with the ordinary product \\(|u|^2u\\). Together with unconditional uniqueness at \\(H^{1/6}\\), this makes the threshold sharp within the singular solution class considered here.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.07866",
  "author_total": 1,
  "authors": [
    {
      "name": "Qirui Peng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0vga8z96gsj48.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.07866",
  "fulltext_url": null,
  "id": "0vga8z96gsj48",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.07866",
  "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": "W7202190331",
  "pdf_url": "https://arxiv.org/pdf/2608.07866",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0vga8z96gsj48.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2608.07866",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.07866"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp non-uniqueness of singular solutions to the one-dimensional periodic cubic nonlinear Schrödinger equation",
  "title_text": "Sharp non-uniqueness of singular solutions to the one-dimensional periodic cubic nonlinear Schrödinger equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/0vga8z96gsj48",
  "venue": "arXiv",
  "versions": []
}