{
  "id": "math/0604278",
  "version": "v1",
  "published": "2006-04-12T14:39:39.000Z",
  "updated": "2006-04-12T14:39:39.000Z",
  "title": "Dirichlet and Neumann Problems for String Equation, Poncelet Problem and Pell-Abel Equation",
  "authors": [
    "Vladimir P. Burskii",
    "Alexei S. Zhedanov"
  ],
  "comment": "Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/",
  "journal": "SIGMA 2 (2006), 041, 5 pages",
  "doi": "10.3842/SIGMA.2006.041",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider conditions for uniqueness of the solution of the Dirichlet or the Neumann problem for 2-dimensional wave equation inside of bi-quadratic algebraic curve. We show that the solution is non-trivial if and only if corresponding Poncelet problem for two conics associated with the curve has periodic trajectory and if and only if corresponding Pell-Abel equation has a solution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-04-12T14:39:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "neumann problem",
      "string equation",
      "wave equation inside",
      "bi-quadratic algebraic curve",
      "corresponding pell-abel equation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}