{
  "id": "2304.02987",
  "version": "v1",
  "published": "2023-04-06T10:47:37.000Z",
  "updated": "2023-04-06T10:47:37.000Z",
  "title": "Quantized vortex dynamics of the nonlinear Schrödinger equation on torus with non-vanishing momentum",
  "authors": [
    "Yongxing Zhu",
    "Weizhu Bao",
    "Huaiyu Jian"
  ],
  "comment": "20 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We derive rigorously the reduced dynamical laws for quantized vortex dynamics of the nonlinear Schr\\\"{o}dinger equation on torus with non-vanishing momentum when the vortex core size {\\epsilon} \\to 0. The reduced dynamical laws are governed by a Hamiltonian flow driven by a renormalized energy. A key ingredient is to construct a new canonical harmonic map to include the effect from the non-vanishing momentum into the dynamics. Finally, some properties of the reduced dynamical law are discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-06T10:47:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q40",
      "35Q55"
    ],
    "keywords": [
      "quantized vortex dynamics",
      "nonlinear schrödinger equation",
      "non-vanishing momentum",
      "reduced dynamical law",
      "hamiltonian flow driven"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}