{
  "id": "2405.08258",
  "version": "v1",
  "published": "2024-05-14T01:12:48.000Z",
  "updated": "2024-05-14T01:12:48.000Z",
  "title": "On special properties of solutions to Camassa-Holm equation and related models",
  "authors": [
    "Christian Hong",
    "Felipe Linares",
    "Gustavo Ponce"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study unique continuation properties of solutions to the b-family of equations. This includes the Camassa-Holm and the Degasperi-Procesi models. We prove that for both, the initial value problem and the periodic boundary value problem, the unique continuation results found in \\cite{LiPo} are optimal. More precisely, the result established there for the constant $c_0=0$ fails for any constant $c_0\\neq 0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-14T01:12:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q35",
      "35B65",
      "76B15"
    ],
    "keywords": [
      "camassa-holm equation",
      "special properties",
      "related models",
      "study unique continuation properties",
      "periodic boundary value problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}