{
  "abstract": "In this paper, we propose an explicit third-order low-regularity integrator for the cubic nonlinear Schrödinger equation on the one-dimensional torus $\\mathbb{T}$. By carefully designing numerical approximations for the integrals in Fourier space, we construct a third-order scheme and provide a rigorous global error analysis. More precisely, we prove that the scheme achieves third-order convergence in $H^{r}(\\mathbb{T})$ for the initial data in $H^{r+4}(\\mathbb{T})$ with $r>1/2$. Furthermore, the third-order convergence in $L^{2}(\\mathbb{T})$ is established for the initial data in $H^{4}(\\mathbb{T})$. Numerical experiments are presented to confirm the theoretical convergence results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34918",
  "author_total": 3,
  "authors": [
    {
      "name": "Shengxin Luo"
    },
    {
      "name": "Bin Wang"
    },
    {
      "name": "Yan Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9aydvcx5z35hn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34918",
  "fulltext_url": null,
  "id": "9aydvcx5z35hn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34918",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2612|Numerical methods for differential equations"
    ]
  ],
  "openalex": "W7223792152",
  "pdf_url": "https://arxiv.org/pdf/2610.34918",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9aydvcx5z35hn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34918",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34918"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "An explicit third-order low-regularity integrator for the cubic nonlinear Schrödinger equation",
  "title_text": "An explicit third-order low-regularity integrator for the cubic nonlinear Schrödinger equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/9aydvcx5z35hn",
  "venue": "arXiv",
  "versions": []
}