{
  "id": "1310.6531",
  "version": "v1",
  "published": "2013-10-24T09:01:50.000Z",
  "updated": "2013-10-24T09:01:50.000Z",
  "title": "Rigorous numerics for NLS: bound states, spectra, and controllability",
  "authors": [
    "Roberto Castelli",
    "Holger Teismann"
  ],
  "comment": "30 pages, 2 figures",
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper it is demonstrated how rigorous numerics may be applied to the one-dimensional nonlinear Schr\\\"odinger equation (NLS); specifically, to determining bound--state solutions and establishing certain spectral properties of the linearization. Since the results are rigorous, they can be used to complete a recent analytical proof [6] of the local exact controllability of NLS.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-24T09:01:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65G99",
      "35Q55",
      "35Q93"
    ],
    "keywords": [
      "rigorous numerics",
      "bound states",
      "local exact controllability",
      "one-dimensional nonlinear",
      "spectral properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.6531C"
    }
  }
}