{
  "id": "2408.05158",
  "version": "v1",
  "published": "2024-08-09T16:29:26.000Z",
  "updated": "2024-08-09T16:29:26.000Z",
  "title": "Trees, trunks, and branches -- bifurcation structure of time-periodic solutions to $u_{tt}-u_{xx}\\pm u^{3}=0$",
  "authors": [
    "Filip Ficek",
    "Maciej Maliborski"
  ],
  "comment": "22 pages, 5 figures",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We propose a systematic approach of analysing the complex structure of time-periodic solutions to the cubic wave equation on interval with Dirichlet boundary conditions first reported in arXiv:2407.16507. Our results complement previous rigorous existence proofs and suggest that solutions exist for any frequency, however, they may be arbitrarily large.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-09T16:29:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B10",
      "35B32",
      "35L71"
    ],
    "keywords": [
      "time-periodic solutions",
      "bifurcation structure",
      "dirichlet boundary conditions first",
      "cubic wave equation",
      "complex structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}