{
  "abstract": "The Whitham equation has given its name to a wider family of nonlocal, nonlinear equations with very weak dispersion, which all feature highest waves. Recent work by Ehrnström, Maehlen and Varholm establishes leading-order asymptotics at the crest of solutions to such Whitham-type equations, and conjectures similar expansions for all derivatives of the solution. By extending their techniques we confirm the conjecture for a range of equations with highest waves of Hölder regularity $C^{s}$ for $s\\in[0.35,1)$. We do this by strong induction, redistributing difference operators to deal with singularities in higher-order derivatives arising from integral convolution kernels. The restriction $s\\geq0.35$ arises solely from the separate argument establishing the zeroth-order asymptotics, which requires a uniform sign estimate that we verify using rigorous interval arithmetic. The higher-order induction itself applies for every $s\\in(0,1)$, so any extension of the zeroth-order result immediately yields the corresponding higher-order expansions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24447",
  "author_total": 1,
  "authors": [
    {
      "name": "Robin Østern Lien"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fja2t0tdk22km.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24447",
  "fulltext_url": null,
  "id": "fja2t0tdk22km",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24447",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2609.24447",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fja2t0tdk22km.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24447",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24447"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Higher-order estimates of highest waves of the Whitham equation",
  "title_text": "Higher-order estimates of highest waves of the Whitham equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/fja2t0tdk22km",
  "venue": "arXiv",
  "versions": []
}