{
  "abstract": "We propose a new formulation of the Korteweg-de Vries equation (KdV) on the real line, via a gauge transform. While KdV and the gauged equation are equivalent for smooth solutions, the latter is better behaved at low regularity in Fourier-Lebesgue spaces. In particular, the admissible regularities go beyond the $H^{-1}$-scale, which is a well-known threshold for KdV. As a byproduct, by reversing the gauge transform, we are able to improve on the known theory for KdV and derive sharp local well-posedness in Fourier-Lebesgue spaces with large integrability exponent. Our strategy is based on an infinite normal form reduction and Fourier restriction estimates, together with a thorough exploitation of algebraic cancellations. Additionally, our method is totally independent of the KdV completely integrable structure, and extends to other non-integrable models with quadratic nonlinearities.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2601.15060",
  "author_total": 3,
  "authors": [
    {
      "name": "Chapouto, Andreia"
    },
    {
      "name": "Correia, Simão"
    },
    {
      "name": "Ramos, João Pedro"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/esvesh5q2c81w.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "esvesh5q2c81w",
  "issns": [],
  "landing_url": "https://hal.science/hal-05851594v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05851594/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/esvesh5q2c81w.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T12:20:54Z",
      "native_id": "hal-05851594",
      "source": "hal",
      "url": "https://hal.science/hal-05851594v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.math",
      "subfield": "general"
    }
  ],
  "title": "Gauge transform for the Korteweg-de Vries equation and well-posedness below the H−1-SCALE",
  "title_text": "Gauge transform for the Korteweg-de Vries equation and well-posedness below the H−1-SCALE",
  "type": "preprint",
  "updated_at": "2026-11-10T12:20:54Z",
  "url": "https://research.draconitic.com/paper/esvesh5q2c81w",
  "venue": "HAL",
  "versions": []
}