{
  "id": "2001.03969",
  "version": "v1",
  "published": "2020-01-12T18:23:24.000Z",
  "updated": "2020-01-12T18:23:24.000Z",
  "title": "Stability of the standing waves of the concentrated NLSE in dimension two",
  "authors": [
    "Riccardo Adami",
    "Raffaele Carlone",
    "Michele Correggi",
    "Lorenzo Tentarelli"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper we will continue the analysis of two dimensional Schr\\\"odinger equation with a fixed, pointwise, nonlinearity started in [2, 13]. In this model, the occurrence of a blow-up phenomenon has two peculiar features: the energy threshold under which all solutions blow up is strictly negative and coincides with the infimum of the energy of the standing waves; there is no critical power nonlinearity, i.e., for every power there exist blow-up solutions. Here we study the stability properties of stationary states to verify whether the anomalies mentioned before have any counterpart on the stability features.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-12T18:23:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "standing waves",
      "concentrated nlse",
      "stationary states",
      "stability properties",
      "blow-up solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}