{
  "abstract": "We classify the multi-solitons, in the positive sense of time, of the focusing energy-critical wave equation in space dimension $5$, more precisely the solutions $u(t,x)$ of the equation \\[ \\partial_t^2 u - Δu - |u|^{\\frac 4{3}} u = 0, \\quad (t,x)\\in [T_0,\\infty)\\times {\\mathbb R}^5, \\] which satisfy the estimate \\[ \\left\\|\\nabla_{t,x} \\left(u(t) - \\sum_{k} W_k(t) \\right) \\right\\|_{L^2} \\lesssim t^{-\\frac12^+} \\quad \\hbox{for all $t\\gg 1$}. \\] Here, $\\{W_k\\}_k$ is any given finite family of traveling waves, based on the explicit ground state solution \\[ W(x) = \\left(1+ \\frac{|x|^2}{15}\\right)^{-\\frac32} \\] with collinear two-by-two different velocities.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09967",
  "author_total": 2,
  "authors": [
    {
      "name": "Yvan Martel"
    },
    {
      "name": "Frank Merle"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b3zfenyhj4jpq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09967",
  "fulltext_url": null,
  "id": "b3zfenyhj4jpq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09967",
  "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",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7212127711",
  "pdf_url": "https://arxiv.org/pdf/2609.09967",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b3zfenyhj4jpq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.09967",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09967"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Classification of multi-solitons in one sense of time for the 5D energy-critical wave equation",
  "title_text": "Classification of multi-solitons in one sense of time for the 5D energy-critical wave equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/b3zfenyhj4jpq",
  "venue": "arXiv",
  "versions": []
}