{
  "id": "1805.03974",
  "version": "v1",
  "published": "2018-05-08T22:10:59.000Z",
  "updated": "2018-05-08T22:10:59.000Z",
  "title": "Solutions of Gross-Pitaevskii Equation with Periodic Potential in Dimension Two",
  "authors": [
    "Yulia Karpeshina",
    "Seonguk Kim",
    "Roman Shterenberg"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1707.01872",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Quasi-periodic solutions of a nonlinear polyharmonic equation for the case $4l>n+1$ in $\\R^n$, $n>1$, are studied. This includes Gross-Pitaevskii equation in dimension two ($l=1,n=2$). It is proven that there is an extensive \"non-resonant\" set ${\\mathcal G}\\subset \\R^n$ 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": "2018-05-08T22:10:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gross-pitaevskii equation",
      "periodic potential",
      "nonlinear polyharmonic equation",
      "solution asymptotically close",
      "plane wave"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}