{
  "id": "2106.00499",
  "version": "v1",
  "published": "2021-06-01T14:06:25.000Z",
  "updated": "2021-06-01T14:06:25.000Z",
  "title": "Weak Sobolev almost periodic solutions for the 1d NLS",
  "authors": [
    "Luca Biasco",
    "Jessica Elisa Massetti",
    "Michela Procesi"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We construct almost periodic solutions of the one dimensional analytic NLS with external parameters. Our solutions have Sobolev regularity both in time and space and typically solve the equation only in a weak sense. This is the first result of this kind in KAM theory for PDEs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-01T14:06:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic solutions",
      "1d nls",
      "weak sobolev",
      "dimensional analytic nls",
      "first result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}