{
  "abstract": "In this paper, we consider the existence of small- and large-amplitude compressible water waves. These are solutions of the two-dimensional free boundary isentropic Euler equations subjected to a constant gravitational force and neglecting the effects of surface tension. We study periodic and solitary waves beneath vacuum as well as front-type solutions of the two-phase problem in a channel. Using local and global bifurcation techniques, we construct large families of these waves beginning at an incompressible solution and treating the Mach number (defined in a suitable sense) as the bifurcation parameter. This gives a rigorous version of the classical Janzen--Rayleigh expansion, but also furnishes solution curves that may limit to transsonic flow.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01883",
  "author_total": 2,
  "authors": [
    {
      "name": "Abba Ramadan"
    },
    {
      "name": "Samuel Walsh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/49q5jxfy85hv4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01883",
  "fulltext_url": null,
  "id": "49q5jxfy85hv4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01883",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.01883",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/49q5jxfy85hv4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01883",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01883"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Compressible steady water waves",
  "title_text": "Compressible steady water waves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/49q5jxfy85hv4",
  "venue": "arXiv",
  "versions": []
}