{
  "abstract": "We study the long-time behavior of the one-dimensional defocusing cubic nonlinear Schrödinger equation with initial data in $L^2(\\mathbb R)$. We first prove that the standard fixed-profile modified-scattering ansatz fails at the unweighted $L^2$ endpoint for the one-dimensional defocusing cubic nonlinear Schrödinger equation. More precisely, there exists a real-valued datum $$u_*\\in L^1(\\mathbb R)\\cap\\bigcap_{m\\in\\mathbb N}H^m(\\mathbb R), \\qquad xu_*\\notin L^2(\\mathbb R).,$$ for which the corrected Fourier profile has no strong $L^2$ limit. Secondly, for every $L^2$ datum, we prove generalized modified scattering: in the physical ray coordinates $x=2tz$, the rescaled solution admits a strong $L^2$ asymptotic representation whose amplitude is the square root of the conserved transmission density and whose unit complex phase is determined by the initial datum.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.02534",
  "author_total": 1,
  "authors": [
    {
      "name": "Xi Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/crbwfrv7sjehm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.02534",
  "fulltext_url": null,
  "id": "crbwfrv7sjehm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.02534",
  "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": "W7172457972",
  "pdf_url": "https://arxiv.org/pdf/2608.02534",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/crbwfrv7sjehm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2608.02534",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.02534"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Failure of fixed-profile modified scattering and generalized modified scattering for the 1D defocusing cubic NLS",
  "title_text": "Failure of fixed-profile modified scattering and generalized modified scattering for the 1D defocusing cubic NLS",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/crbwfrv7sjehm",
  "venue": "arXiv",
  "versions": []
}