{
  "abstract": "We construct infinite-time Sobolev cascades for the cubic nonlinear half-wave equation on the real line. For $\\frac12<s\\leq1$ and $0\\leqκ<2s(2s-1)/(4s-1)$, spatial gluing of permanently saturated two-soliton packets gives a dense set of strictly mass-subthreshold data for which $\\|u(t)\\|_{H^s}/(1+t)^κ\\to\\infty$ in the focusing case. A second construction replicates finite-burst Szegő packets without rescaling. It yields a dense $G_δ$ subset of $H^\\infty(\\mathbb R)$ whose solutions perform logarithmic cascades in every $H^s$ with $s>\\frac12$ in the focusing case and in the defocusing case.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27813",
  "author_total": 1,
  "authors": [
    {
      "name": "Xi Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9yav5wg2kt8dn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27813",
  "fulltext_url": null,
  "id": "9yav5wg2kt8dn",
  "issns": [],
  "landing_url": "https://hal.science/hal-05731979v1",
  "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": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7203961387",
  "pdf_url": "https://hal.science/hal-05731979/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9yav5wg2kt8dn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:21Z",
      "native_id": "hal-05731979",
      "source": "hal",
      "url": "https://hal.science/hal-05731979v1"
    },
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27813",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27813"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "INFINITE CASCADES FOR THE CUBIC NONLINEAR HALF-WAVE EQUATION ON THE LINE",
  "title_text": "INFINITE CASCADES FOR THE CUBIC NONLINEAR HALF-WAVE EQUATION ON THE LINE",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/9yav5wg2kt8dn",
  "venue": "HAL",
  "versions": []
}