{
  "id": "2202.06792",
  "version": "v1",
  "published": "2022-02-14T15:13:15.000Z",
  "updated": "2022-02-14T15:13:15.000Z",
  "title": "Solutions of Gross-Pitaevskii Equation with Periodic Potential in Dimension Three",
  "authors": [
    "Yulia Karpeshina",
    "Seonguk Kim",
    "Roman Shterenberg"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1805.03974, arXiv:1707.01872",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Quasi-periodic solutions of the Gross-Pitaevskii equation with a periodic potential in dimension three are studied. It is proven that there is an extensive \"non-resonant\" set ${\\mathcal G} \\subset \\mathbb{R}^3$ such that for every $\\vec k\\in \\mathcal G$ there is a solution asymptotically close to a plane wave $Ae^{i\\langle{ \\vec{k}, \\vec{x} }\\rangle}$ as $|\\vec k|\\to \\infty $, given $A$ is sufficiently small.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-14T15:13:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic potential",
      "gross-pitaevskii equation",
      "quasi-periodic solutions",
      "solution asymptotically close",
      "plane wave"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}