{
  "abstract": "We study a class of complex-valued KdV-type equations with cubic second-order derivative nonlinearities and arbitrary complex coefficients. For sufficiently small initial data in $L^2$, we prove local well-posedness in $H^s(\\mathbb R)$ for $s\\ge3/4$. The key ingredient is a family of dyadic resolution spaces $Z_k=X_k+Y_k$, designed to overcome the logarithmic divergence arising from high$*$low$*$low interactions in which both derivatives fall on the highest-frequency factor. For the completely integrable third-order Kaup--Newell flow, we establish global-in-time $H^s(\\mathbb R)$ bounds for $0\\le s<1$ and global well-posedness in $H^s(\\mathbb R)$ for every $s\\ge3/4$, with no smallness assumption on the initial data.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28975",
  "author_total": 3,
  "authors": [
    {
      "name": "Mingjuan Chen"
    },
    {
      "name": "Ting Chen"
    },
    {
      "name": "Zhong Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/04sd2q5rqv87c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28975",
  "fulltext_url": null,
  "id": "04sd2q5rqv87c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28975",
  "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",
      "math.AP"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7214342247",
  "pdf_url": "https://arxiv.org/pdf/2609.28975",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/04sd2q5rqv87c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.28975",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28975"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Well-Posedness for KdV-Type Equations with Second-Order Derivative Nonlinearities",
  "title_text": "Well-Posedness for KdV-Type Equations with Second-Order Derivative Nonlinearities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/04sd2q5rqv87c",
  "venue": "arXiv",
  "versions": []
}