{
  "id": "1211.5553",
  "version": "v1",
  "published": "2012-11-23T17:01:33.000Z",
  "updated": "2012-11-23T17:01:33.000Z",
  "title": "On the existence of hylomorphic vortices in the nonlinear Klein-Gordon equation",
  "authors": [
    "Jacopo Bellazzini",
    "Vieri Benci",
    "Claudio Bonanno",
    "Edoardo Sinibaldi"
  ],
  "comment": "23 pages, 5 figures",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper we prove the existence of vortices, namely standing waves with non null angular momentum, for the nonlinear Klein-Gordon equation in dimension $N\\geq 3$. We show with variational methods that the existence of these kind of solutions, that we have called \\emph{hylomorphic vortices}, depends on a suitable energy-charge ratio. Our variational approach turns out to be useful for numerical investigations as well. In particular, some results in dimension N=2 are reported, namely exemplificative vortex profiles by varying charge and angular momentum, together with relevant trends for vortex frequency and energy-charge ratio. The stability problem for hylomorphic vortices is also addressed. In the absence of conclusive analytical results, vortex evolution is numerically investigated: the obtained results suggest that, contrarily to solitons with null angular momentum, vortex are unstable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-23T17:01:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear klein-gordon equation",
      "hylomorphic vortices",
      "energy-charge ratio",
      "non null angular momentum",
      "variational approach turns"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1203747,
      "adsabs": "2012arXiv1211.5553B"
    }
  }
}