{
  "id": "1011.1776",
  "version": "v1",
  "published": "2010-11-08T11:35:12.000Z",
  "updated": "2010-11-08T11:35:12.000Z",
  "title": "Global dynamics above the ground state energy for the one-dimensional NLKG equation",
  "authors": [
    "Joachim Krieger",
    "Kenji Nakanishi",
    "Wilhelm Schlag"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we obtain a global characterization of the dynamics of even solutions to the one-dimensional nonlinear Klein-Gordon (NLKG) equation on the line with focusing nonlinearity |u|^{p-1}u, p>5, provided their energy exceeds that of the ground state only sightly. The method is the same as in the three-dimensional case arXiv:1005.4894, the major difference being in the construction of the center-stable manifold. The difficulty there lies with the weak dispersive decay of 1-dimensional NLKG. In order to address this specific issue, we establish local dispersive estimates for the perturbed linear Klein-Gordon equation, similar to those of Mizumachi arXiv:math/0605031. The essential ingredient for the latter class of estimates is the absence of a threshold resonance of the linearized operator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-11-08T11:35:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L70",
      "35Q55"
    ],
    "keywords": [
      "one-dimensional nlkg equation",
      "ground state energy",
      "global dynamics",
      "one-dimensional nonlinear klein-gordon",
      "perturbed linear klein-gordon equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.1776K"
    }
  }
}