{
  "abstract": "We consider the damped nonlinear Klein-Gordon equation \\begin{align*} \\partial_t^2u-Δu+2α\\partial_tu+u-|u|^{p-1}u=0 \\end{align*} on $\\mathbb{R}^d$, where $α>0$, $2\\leq d\\leq5$, and $p>2$ is in the energy-subcritical range. We classify global solutions that converge to a superposition of two positive and two negative translates of the ground state, without imposing any symmetry, coplanarity, or a priori geometric condition on their centers. We prove that every such four-soliton configuration is asymptotically either an alternating collinear configuration or an expanding rhombus with alternating signs. We further determine the precise long-time asymptotics of all four centers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13207",
  "author_total": 1,
  "authors": [
    {
      "name": "Ishizuka Kenjiro"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/08prs6k959xtv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13207",
  "fulltext_url": null,
  "id": "08prs6k959xtv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13207",
  "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",
      "math.AP"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7213280107",
  "pdf_url": "https://arxiv.org/pdf/2609.13207",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/08prs6k959xtv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13207",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13207"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Classification and long-time asymptotics of $(2,2)$-sign solitons for the damped nonlinear Klein-Gordon equation",
  "title_text": "Classification and long-time asymptotics of (2,2)-sign solitons for the damped nonlinear Klein-Gordon equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/08prs6k959xtv",
  "venue": "arXiv",
  "versions": []
}