{
  "id": "2303.16269",
  "version": "v1",
  "published": "2023-03-28T19:29:09.000Z",
  "updated": "2023-03-28T19:29:09.000Z",
  "title": "Scattering for the defocusing NLS on the line with variable coefficients",
  "authors": [
    "Piero D'Ancona",
    "Angelo Zanni"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove $H^{1}$ scattering for a defocusing NLS on the line with fully variable coefficients. The result is proved by adapting the Kenig--Merle scheme to a non translation invariant setting. In addition, we give an abstract version of the scheme which can be applied to other operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-28T19:29:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "defocusing nls",
      "scattering",
      "abstract version",
      "non translation invariant setting",
      "kenig-merle scheme"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}