{
  "abstract": "We obtain the leading term in the solution of the Cauchy problem for the Benjamin-Ono equation in the limit t → +∞ with x = O(t^(1/2) ). We show that the rate of decay exceeds that of self-similar solutions and obtain an explicit universal profile for the decaying solution, relating it to the linearization of the profile equation for self-similar solutions. The proof assumes a class of rational initial data u_0 in L^2 (R) ∩ L^1 (R) that exhibit generic behavior of the reflection coefficient at the origin.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.02989",
  "author_total": 3,
  "authors": [
    {
      "name": "Louise Gassot"
    },
    {
      "name": "Patrick Gérard"
    },
    {
      "name": "Peter D. Miller"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6mden24t40qdq.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "6mden24t40qdq",
  "issns": [],
  "landing_url": "https://hal.science/hal-05765501v1",
  "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"
    ],
    [
      "hal",
      "1.math.math-ap"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05765501/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-06-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6mden24t40qdq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "hal-05765501",
      "source": "hal",
      "url": "https://hal.science/hal-05765501v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-ap",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Benjamin-Ono Equation in the Long-Time Limit: Linearized Self-Similar Universality",
  "title_text": "The Benjamin-Ono Equation in the Long-Time Limit: Linearized Self-Similar Universality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:41Z",
  "url": "https://research.draconitic.com/paper/6mden24t40qdq",
  "venue": "HAL",
  "versions": []
}