{
  "id": "0905.1848",
  "version": "v3",
  "published": "2009-05-12T13:46:38.000Z",
  "updated": "2014-11-24T16:19:27.000Z",
  "title": "Existence and stability of solitons for the nonlinear Schrödinger equation on hyperbolic space",
  "authors": [
    "Hans Christianson",
    "Jeremy Marzuola"
  ],
  "comment": "As noted in a recent work of Banica-Duyckaerts (arXiv:1411.0846), Section 5 should read that for sufficiently large mass, sub-critical problems can be solved via energy minimization for all d \\geq 2 and as a result Cazenave-Lions results can be applied in Section 6 with the same restriction. These requirements were addressed by the subsequent work with Metcalfe and Taylor in arXiv:1203.3612",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the existence and stability of ground state solutions or solitons to a nonlinear stationary equation on hyperbolic space. The method of concentration compactness applies and shows that the results correlate strongly to those of Euclidean space.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-06-22T20:13:58.000Z",
      "comment": "Updated references; minor typos corrected",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-11-24T16:19:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "35Q51"
    ],
    "keywords": [
      "nonlinear schrödinger equation",
      "hyperbolic space",
      "ground state solutions",
      "concentration compactness applies",
      "nonlinear stationary equation"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/0951-7715/23/1/005",
      "journal": "Nonlinearity",
      "year": 2010,
      "month": "Jan",
      "volume": 23,
      "number": 1,
      "pages": 89
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010Nonli..23...89C"
    }
  }
}