{
  "id": "2210.08417",
  "version": "v1",
  "published": "2022-10-16T02:46:35.000Z",
  "updated": "2022-10-16T02:46:35.000Z",
  "title": "The Fokas-Lenells equation on the line: Global well-posedness with solitons",
  "authors": [
    "Qiaoyuan Cheng",
    "Engui Fan"
  ],
  "comment": "30 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper, we prove the existence of global solutions in $H^3(\\mathbb{R})\\cap H^{2,1}(\\mathbb{R})$ to the Fokas-Lenells (FL) equation on the line when the initial data includes solitons.A key tool in proving this result is a newly modified Darboux transformation, which adds or subtracts a soliton with given spectral and scattering parameters. In this way the inverse scattering transform technique is then applied to establish the global well-posedness of initial value problem with a finite number of solitons based on our previous results on the global well-posedness of the FL equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-16T02:46:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35P25",
      "35Q51",
      "35Q15",
      "35A01",
      "35G25"
    ],
    "keywords": [
      "global well-posedness",
      "fokas-lenells equation",
      "initial value problem",
      "inverse scattering transform technique",
      "fl equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}