{
  "id": "0908.3648",
  "version": "v2",
  "published": "2009-08-25T16:35:44.000Z",
  "updated": "2009-08-26T09:57:58.000Z",
  "title": "Numerical computation of soliton dynamics for NLS equations in a driving potential",
  "authors": [
    "Marco Caliari",
    "Marco Squassina"
  ],
  "comment": "13 pages, 4 figures",
  "categories": [
    "math.NA"
  ],
  "abstract": "We provide some numerical computations for the soliton dynamics of the nonlinear Schr\\\"odinger equation with an external potential. After computing the ground state solution $r$ of a related elliptic equation we show that, in the semi-classical regime, the center of mass of the solution with initial datum modelled on $r$ is driven by the solution of a Newtonian type law. Finally, we provide some examples and analyze the numerical errors in the two dimensional case when $V$ is an harmonic potential.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-08-26T09:57:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q40",
      "58E30",
      "81Q05",
      "81Q20",
      "37N30"
    ],
    "keywords": [
      "soliton dynamics",
      "numerical computation",
      "nls equations",
      "driving potential",
      "newtonian type law"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.3648C"
    }
  }
}