{
  "id": "1105.3903",
  "version": "v1",
  "published": "2011-05-19T15:00:00.000Z",
  "updated": "2011-05-19T15:00:00.000Z",
  "title": "The Novikov-Veselov Equation and the Inverse Scattering Method, Part I: Analysis",
  "authors": [
    "Matti Lassas",
    "Jennifer L Mueller",
    "Samuli Siltanen",
    "Andreas Stahel"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The Novikov-Veselov (NV) equation is a (2+1)-dimensional nonlinear evolution equation that generalizes the (1+1)-dimensional Korteweg-deVries (KdV) equation. Solution of the NV equation using the inverse scattering method has been discussed in the literature, but only formally (or with smallness assumptions in case of nonzero energy) because of the possibility of exceptional points, or singularities in the scattering data. In this work, absence of exceptional points is proved at zero energy for evolutions with compactly supported, smooth and rotationally symmetric initial data of the conductivity type: $q_0=\\gamma^{-1/2}\\Delta\\gamma^{1/2}$ with a strictly positive function $\\gamma$. The inverse scattering evolution is shown to be well-defined, real-valued, and preserving conductivity-type. There is no smallness assumption on the initial data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-05-19T15:00:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37K15"
    ],
    "keywords": [
      "inverse scattering method",
      "novikov-veselov equation",
      "smallness assumption",
      "exceptional points",
      "nonlinear evolution equation"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.physd.2012.04.010",
      "journal": "Physica D Nonlinear Phenomena",
      "year": 2012,
      "month": "Aug",
      "volume": 241,
      "number": 16,
      "pages": 1322
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012PhyD..241.1322L"
    }
  }
}