{
  "id": "2311.15336",
  "version": "v1",
  "published": "2023-11-26T15:46:50.000Z",
  "updated": "2023-11-26T15:46:50.000Z",
  "title": "On the first bifurcation of solitary waves",
  "authors": [
    "Vladimir Kozlov"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2307.05573, arXiv:2303.11440",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider solitary water waves on the vorticity flow in a two-dimensional channel of finite depth. The main object of study is a branch of solitary waves starting from a laminar flow and then approaching an extreme wave. We prove that there always exists a bifurcation point on such branches. Moreover, the crossing number of the first bifurcation point is 1, i.e. the bifurcation occurs at a simple eigenvalue.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-26T15:46:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "solitary waves",
      "solitary water waves",
      "first bifurcation point",
      "bifurcation occurs",
      "vorticity flow"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}