{
  "id": "2307.06015",
  "version": "v1",
  "published": "2023-07-12T08:57:46.000Z",
  "updated": "2023-07-12T08:57:46.000Z",
  "title": "Construction of minimizing travelling waves for the Gross-Pitaevskii equation on $\\mathbb{R} \\times \\mathbb{T}$",
  "authors": [
    "André de Laire",
    "Philippe Gravejat",
    "Didier Smets"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "As a sequel to our previous analysis in [9] arXiv:2202.09411 on the Gross-Pitaevskii equation on the product space $\\mathbb{R} \\times \\mathbb{T}$, we construct a branch of finite energy travelling waves as minimizers of the Ginzburg-Landau energy at fixed momentum. We deduce that minimizers are precisely the planar dark solitons when the length of the transverse direction is less than a critical value, and that they are genuinely two-dimensional solutions otherwise. The proof of the existence of minimizers is based on the compactness of minimizing sequences, relying on a new symmetrization argument that is well-suited to the periodic setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-12T08:57:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "35J20",
      "35C07",
      "37K05",
      "35C08",
      "35A01",
      "37K40"
    ],
    "keywords": [
      "gross-pitaevskii equation",
      "minimizing travelling waves",
      "construction",
      "finite energy travelling waves",
      "minimizers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}