{
  "abstract": "We develop a flow-map framework for nonlinear transport equations, comprising a self-consistent exact frozen flow and its numerical realization. An exponential--pullback identity represents each frozen transport exponential in a commutator-free exponential integrator as the pullback induced by its exact backward characteristic map. Composing these maps defines the self-consistent exact frozen flow, a time-discrete construction with autonomous frozen fields formed from linear combinations of transport fields evaluated at the stage approximations. A local freezing-error identity and a one-step estimate for the Lie--Euler Vlasov--Poisson update separate field variation, field approximation, and characteristic integration errors; these estimates do not assert global PDE convergence. We specialize this construction to the Vlasov--Poisson system and obtain the self-consistent numerical flow through velocity-space quadrature, a discrete Poisson solve, field interpolation, and numerical integration of the frozen characteristic equations. Under suitable regularity assumptions, we prove that the self-consistent exact frozen flow for this system is a volume-preserving diffeomorphism. Temporal self-convergence tests on Vlasov--Poisson and guiding-center benchmarks yield rates consistent with the design orders and illustrate conservation behavior and the evolution of solution structures in long-time simulations with large time steps.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35327",
  "author_total": 2,
  "authors": [
    {
      "name": "Xiaofeng Cai"
    },
    {
      "name": "Linghui Kong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cme6wf5abfkyw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35327",
  "fulltext_url": null,
  "id": "cme6wf5abfkyw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35327",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "physics.plasm-ph"
    ],
    [
      "openalex",
      "2612|Numerical methods for differential equations"
    ]
  ],
  "openalex": "W7223871975",
  "pdf_url": "https://arxiv.org/pdf/2610.35327",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cme6wf5abfkyw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.35327",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35327"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.plasm-ph",
      "subfield": "plasma"
    }
  ],
  "title": "Self-consistent flow maps based on commutator-free exponential integrators",
  "title_text": "Self-consistent flow maps based on commutator-free exponential integrators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/cme6wf5abfkyw",
  "venue": "arXiv",
  "versions": []
}