{
  "id": "1605.09095",
  "version": "v1",
  "published": "2016-05-30T03:46:49.000Z",
  "updated": "2016-05-30T03:46:49.000Z",
  "title": "Orbital stability and uniqueness of the ground state for NLS in dimension one",
  "authors": [
    "Daniele Garrisi",
    "Vladimir Georgiev"
  ],
  "comment": "22 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove that standing-waves solutions to the non-linear Schr\\\"odinger equation in dimension one whose profiles can be obtained as minima of the energy over the mass, are orbitally stable and non-degenerate, provided the non-linear term $ G $ satisfies a Euler differential inequality. When the non-linear term $ G $ is a combined pure power-type, then there is only one positive, symmetric minimum of prescribed mass.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-30T03:46:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "47J35"
    ],
    "keywords": [
      "ground state",
      "orbital stability",
      "uniqueness",
      "non-linear term",
      "euler differential inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}