{
  "abstract": "We propose a potential projection (PP) method for the nonlinear Schrödinger equation (NLSE) with low-regularity and singular potentials by replacing the potential with its Fourier projection (truncated Fourier series). This gives rise to an NLSE with projected potential (NLSEwPP). We rigorously establish its well-posedness under low-regularity potentials, and its convergence to the original NLSE. The NLSEwPP is then directly discretized by the standard time-splitting Fourier pseudospectral (TS-FP) method with the mesh size chosen according to the potential projection parameter, resulting in the fully discrete TS-PP-FP method. Numerically, TS-PP-FP consistently achieves optimal temporal and spatial convergence rates with respect to the regularity of the exact solution under low-regularity and even singular potentials. Compared with the time-splitting Fourier spectral method, TS-PP-FP attains the same convergence rates at significantly lower computational cost and preserves the mass conservation and time symmetry (that are lost in the Fourier spectral discretization of the time-splitting method); compared with the time-splitting FP method, it is substantially more accurate for low-regularity potentials with the same computational cost.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19430",
  "author_total": 3,
  "authors": [
    {
      "name": "Weizhu Bao"
    },
    {
      "name": "Qingyuan Sun"
    },
    {
      "name": "Chushan Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1s9zyprbmkm3d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19430",
  "fulltext_url": null,
  "id": "1s9zyprbmkm3d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19430",
  "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": "W7222226226",
  "pdf_url": "https://arxiv.org/pdf/2610.19430",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1s9zyprbmkm3d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19430",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19430"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A potential projection method for the nonlinear Schrödinger equation with low regularity potential",
  "title_text": "A potential projection method for the nonlinear Schrödinger equation with low regularity potential",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/1s9zyprbmkm3d",
  "venue": "arXiv",
  "versions": []
}