{
  "abstract": "We prove the existence of rogue waves and breathers in nonlinear lattice wave equations including the nonlinear Klein--Gordon and the FPUT lattice (with added local forces). The main feature of our lattice wave equation is that the kinetic part $\\frac{\\mathrm{d}^2}{\\mathrm{d}t^2}$ is multiplied by a non-constant function $\\frac{1}{d(t)}$ such that gaps in the spectrum of $\\frac{1}{d(t)}\\frac{\\mathrm{d}^2}{\\mathrm{d}t^2}$ open wide enough to include the spectrum of the spatial linear operator. We find solutions as critical points of an indefinite functional using a saddle-point method combined with concentration-compactness arguments. In case of temporally $T$-periodic coefficients and under identical assumptions as for rogue waves, the same variational method also provides existence of breather solutions whose temporal period is an arbitrary prescribed integer multiple of $T$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26456",
  "author_total": 2,
  "authors": [
    {
      "name": "Julia Henninger"
    },
    {
      "name": "Wolfgang Reichel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5tgpen5h53gr7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26456",
  "fulltext_url": null,
  "id": "5tgpen5h53gr7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26456",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7214128327",
  "pdf_url": "https://arxiv.org/pdf/2609.26456",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5tgpen5h53gr7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.26456",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26456"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Homoclinics, rogue waves and breathers in nonlinear lattice wave equations",
  "title_text": "Homoclinics, rogue waves and breathers in nonlinear lattice wave equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/5tgpen5h53gr7",
  "venue": "arXiv",
  "versions": []
}