{
  "abstract": "Nonlinear coupled dispersive models arise in numerous physical settings, including quantum electrodynamics, nonlinear optics, and plasma dynamics. In the nonrelativistic limit, such systems exhibit rapid temporal oscillations of wavelength $\\mathcal{O}(\\varepsilon^{2})$, controlled by a dimensionless parameter $0<\\varepsilon\\ll 1$. Moreover, owing to the Yukawa-coupled interaction terms, numerical schemes that simultaneously achieve high-order uniform accuracy and approximately preserve the mass and the energy are essential for reliable simulations. In this work, we propose a class of fully discrete schemes for nonlinear coupled dispersive models in the nonrelativistic regime that achieve higher-order uniform accuracy and approximately preserve both invariants over long times. Spatial discretization is based on the Fourier pseudospectral method, and time advancement employs two-scale exponential Runge-Kutta methods. Numerical experiments on the highly oscillatory Klein-Gordon-Dirac and Klein-Gordon-Schrödinger equations in one, two, and three dimensions confirm that the resulting schemes attain the theoretically predicted uniform accuracy and the long-time near-conservation of both invariants.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16044",
  "author_total": 3,
  "authors": [
    {
      "name": "Lina Wang"
    },
    {
      "name": "Jiyong Li"
    },
    {
      "name": "Bin Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1rb2vgfgqhgfg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16044",
  "fulltext_url": null,
  "id": "1rb2vgfgqhgfg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16044",
  "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": "W7221819464",
  "pdf_url": "https://arxiv.org/pdf/2610.16044",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1rb2vgfgqhgfg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.16044",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16044"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "High-order uniformly accurate fully discrete schemes with long time near-conservations for two nonlinear coupled dispersive models in the nonrelativistic regime",
  "title_text": "High-order uniformly accurate fully discrete schemes with long time near-conservations for two nonlinear coupled dispersive models in the nonrelativistic regime",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/1rb2vgfgqhgfg",
  "venue": "arXiv",
  "versions": []
}