{
  "id": "1904.06741",
  "version": "v1",
  "published": "2019-04-14T19:04:05.000Z",
  "updated": "2019-04-14T19:04:05.000Z",
  "title": "Connection Formulae for Asymptotics of the Fifth Painlevé Transcendent on the Imaginary Axis: I",
  "authors": [
    "F. V. Andreev",
    "A. V. Kitaev"
  ],
  "comment": "71 pages, 30 figures",
  "categories": [
    "math.CA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Leading terms of asymptotic expansions for the general complex solutions of the fifth Painlev\\'e equation as $t\\to\\imath\\infty$ are found. These asymptotics are parameterized by monodromy data of the associated linear ODE. $$ \\frac{d}{d\\lambda}Y= \\left(\\frac t2\\sigma_3 + \\frac{A_0}\\lambda+\\frac{A_1}{\\lambda-1}\\right)Y. $$ The parametrization allows one to derive connection formulas for the asymptotics. We provide numerical verification of the results. Important special cases of the connection formulas are also considered.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-14T19:04:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34M55",
      "33E17",
      "34M40",
      "34M35",
      "34E20"
    ],
    "keywords": [
      "connection formulae",
      "imaginary axis",
      "transcendent",
      "general complex solutions",
      "fifth painleve equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 71,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}