{
  "id": "2002.00399",
  "version": "v1",
  "published": "2020-02-02T14:21:24.000Z",
  "updated": "2020-02-02T14:21:24.000Z",
  "title": "Non-uniqueness for the ab-family of equations",
  "authors": [
    "John Holmes",
    "Rajan Puri"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the cubic ab-family of equations, which includes both the Fokas-Olver-Rosenau-Qiao (FORQ) and the Novikov (NE) equations. For $a\\neq0$, it is proved that there exist initial data in the Sobolev space $H^s$, $s<3/2$, with non-unique solutions. Multiple solutions are constructed by studying the collision of 2-peakon solutions. Furthermore, we prove the novel phenomenon that for some members of the family, collision between 2-peakons can occur even if the \"faster\" peakon is in front of the \"slower\" peakon.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-02T14:21:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q35"
    ],
    "keywords": [
      "non-uniqueness",
      "sobolev space",
      "initial data",
      "multiple solutions",
      "novel phenomenon"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}