{
  "id": "2109.06384",
  "version": "v1",
  "published": "2021-09-14T01:16:12.000Z",
  "updated": "2021-09-14T01:16:12.000Z",
  "title": "Long time asymptotic for the Wadati-Konno-Ichikawa equation with finite density initial data",
  "authors": [
    "Zhi-Qiang Li",
    "Shou-Fu Tian",
    "Jin-Jie Yang"
  ],
  "comment": "40 pages, 5 figures",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "In this work, we investigate the Cauchy problem of the Wadati-Konno-Ichikawa (WKI) equation with finite density initial data. Employing the $\\bar{\\partial}$-generalization of Deift-Zhou nonlinear steepest descent method, we derive the long time asymptotic behavior of the solution $q(x,t)$ in space-time soliton region. Based on the resulting asymptotic behavior, the asymptotic approximation of the WKI equation is characterized with the soliton term confirmed by $N(I)$-soliton on discrete spectrum and the $t^{-\\frac{1}{2}}$ leading order term on continuous spectrum with residual error up to $O(t^{-\\frac{3}{4}})$. Our results also confirm the soliton resolution conjecture for the WKI equation with finite density initial data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-14T01:16:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite density initial data",
      "long time asymptotic",
      "wadati-konno-ichikawa equation",
      "deift-zhou nonlinear steepest descent method",
      "wki equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}