{
  "id": "1412.3149",
  "version": "v1",
  "published": "2014-12-09T22:59:54.000Z",
  "updated": "2014-12-09T22:59:54.000Z",
  "title": "The defocusing nonlinear Schrödinger equation with $t$-periodic data: New exact solutions",
  "authors": [
    "Jonatan Lenells"
  ],
  "comment": "25 pages",
  "categories": [
    "math.AP",
    "nlin.SI"
  ],
  "abstract": "We consider solutions of the defocusing nonlinear Schr\\\"odinger (NLS) equation on the half-line whose Dirichlet and Neumann boundary values become periodic for sufficiently large $t$. We prove a theorem which, modulo certain assumptions, characterizes the pairs of periodic functions which can arise as Dirichlet and Neumann values for large $t$ in this way. The theorem also provides a constructive way of determining explicit solutions with the given periodic boundary values. Hence our approach leads to a class of new exact solutions of the defocusing NLS equation on the half-line.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-09T22:59:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "37K15"
    ],
    "keywords": [
      "defocusing nonlinear schrödinger equation",
      "exact solutions",
      "periodic data",
      "periodic boundary values",
      "neumann boundary values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.3149L"
    }
  }
}