{
  "abstract": "We give a constructive representation of the solution of the KdV equation $u_t=-u_{xxx}+6uu_x$ on $\\mathbb R$ for real initial data in $H^3(\\mathbb R)$. The approximations couple an exact, unitary centered-difference Chernoff product for the Airy group with a skew-symmetric discretization of the quadratic term, and are computed by Picard iteration; they preserve the $L^2$ norm exactly, as does the limit. A two-mesh Cauchy argument shows that the whole sequence converges in $C([0,T];H^2)$, at rate $O(n^{-\\frac{2(s-2)}5})$ for $H^s$ data ($3\\leq s\\leq 7$), and in $L^2$ at rate $O(n^{-6/5})$ for $H^3$ data. This scheme, to the best of our knowledge, is novel and is of independent interest. As a by-product we obtain existence and uniqueness of strong solutions, Lipschitz dependence on the data in the $H^2$ norm, uniformly on bounded subsets of $H^3$ and compact time intervals, and joint locally Lipschitz dependence of $(t,f)\\mapsto S(t)f$ into $L^2$; the classical conservation laws extend the flow globally in time.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31634",
  "author_total": 1,
  "authors": [
    {
      "name": "Comlan Edmond Koudjinan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0d1x0z7v25arr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31634",
  "fulltext_url": null,
  "id": "0d1x0z7v25arr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31634",
  "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": "W7223322465",
  "pdf_url": "https://arxiv.org/pdf/2610.31634",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0d1x0z7v25arr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31634",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31634"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Quantitative constructive representation of the KdV flow in $H^3$ via $L^2$-energy-preserving centered-difference Chernoff approximations and Picard iteration",
  "title_text": "Quantitative constructive representation of the KdV flow in H^3 via L^2-energy-preserving centered-difference Chernoff approximations and Picard iteration",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/0d1x0z7v25arr",
  "venue": "arXiv",
  "versions": []
}