{
  "abstract": "A unidirectional reduction of the deep-water surface gravity wave problem is derived in physical space using real variables. By employing a near-identity canonical transformation, cubic interactions are eliminated from the Hamiltonian, resulting in a bidirectional system analogous to the 1D Zakharov equation. An exact factorization of the linear dynamics then selects the rightward-propagating branch, which is carried to second order in the wave steepness, yielding a single nonlocal evolution equation with full linear dispersion. The model admits an exact monochromatic solution whose reconstructed surface elevation is the third-order Stokes wave, and a multiple-scales analysis recovers the Dysthe envelope equation complete with its nonlocal mean-flow term. The equation also admits exact breather solutions, whose profiles agree closely with those of the super compact equation. Dropping the sub-leading nonlinear terms that vanish on the resonant manifold provides a more compact variant suitable for analytical study. Numerical comparisons show that both formulations track the fully nonlinear Euler dynamics closely through modulational-instability recurrence and broadband focusing up to moderate wave steepness.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.24997",
  "author_total": 1,
  "authors": [
    {
      "name": "Päivo Simson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7twq9gvkrkn26.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.24997",
  "fulltext_url": null,
  "id": "7twq9gvkrkn26",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.24997",
  "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",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "3109|Nonlinear Waves and Solitons"
    ]
  ],
  "openalex": "W7162423189",
  "pdf_url": "https://arxiv.org/pdf/2605.24997",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7twq9gvkrkn26.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2605.24997",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.24997"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "A real-variable unidirectional reduction of deep-water gravity waves",
  "title_text": "A real-variable unidirectional reduction of deep-water gravity waves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:41Z",
  "url": "https://research.draconitic.com/paper/7twq9gvkrkn26",
  "venue": "arXiv",
  "versions": []
}