{
  "id": "1802.08133",
  "version": "v1",
  "published": "2018-02-16T03:11:05.000Z",
  "updated": "2018-02-16T03:11:05.000Z",
  "title": "Reducibility for wave equations of finitely smooth potential with periodic boundary conditions",
  "authors": [
    "Jing Li",
    "Yingte Sun",
    "Bing Xie"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1706.06713",
  "categories": [
    "math.DS"
  ],
  "abstract": "In the present paper, the reducibility is derived for the wave equations with finitely smooth and time-quasi-periodic potential subjects to periodic boundary conditions. More exactly, the linear wave equation $u_{tt}-u_{xx}+Mu+\\varepsilon (V_0(\\omega t)u_{xx}+V(\\omega t, x)u)=0,\\;x\\in \\mathbb{R}/2\\pi \\mathbb{Z}$ can be reduced to a linear Hamiltonian system of a constant coefficient operator which is of pure imaginary point spectrum set, where $V$ is finitely smooth in $(t, x)$, quasi-periodic in time $t$ with Diophantine frequency $\\omega\\in \\mathbb{R}^{n},$ and $V_0$ is finitely smooth and quasi-periodic in time $t$ with Diophantine frequency $\\omega\\in \\mathbb{R}^{n},$ Moreover, it is proved that the corresponding wave operator possesses the property of pure point spectra and zero Lyapunov exponent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-16T03:11:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic boundary conditions",
      "wave equation",
      "finitely smooth potential",
      "pure imaginary point spectrum set",
      "reducibility"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}