{
  "id": "1703.04888",
  "version": "v1",
  "published": "2017-03-15T02:29:09.000Z",
  "updated": "2017-03-15T02:29:09.000Z",
  "title": "Modified scattering for the Klein-Gordon equation with the critical nonlinearity in three dimensions",
  "authors": [
    "Satoshi Masaki",
    "Jun-ichi Segata"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we consider the final state problem for the nonlinear Klein-Gordon equation (NLKG) with a critical nonlinearity in three space dimensions. We prove that for a given asymptotic profile, there exists a solution to (NLKG) which converges to given asymptotic profile as t to infinity. Here the asymptotic profile is given by the leading term of the solution to the linear Klein-Gordon equation with a logarithmic phase correction. Construction of a suitable approximate solution is based on the combination of Fourier series expansion for the nonlinearity used in our previous paper and smooth modification of phase correction by Ginibre-Ozawa.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-15T02:29:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L71",
      "35B40",
      "81Q05"
    ],
    "keywords": [
      "critical nonlinearity",
      "modified scattering",
      "asymptotic profile",
      "final state problem",
      "logarithmic phase correction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}