{
  "id": "1103.2392",
  "version": "v3",
  "published": "2011-03-11T22:36:17.000Z",
  "updated": "2011-08-23T15:06:11.000Z",
  "title": "On a theory of vessels and the inverse scattering",
  "authors": [
    "A. Melnikov"
  ],
  "comment": "37 pages",
  "categories": [
    "math.CA",
    "math-ph",
    "math.CV",
    "math.MP",
    "math.SP"
  ],
  "abstract": "In this paper we present a theory of vessels and its application to the classical inverse scattering of the Sturm-Liouville differential equation. The classical inverse scattering theory, including all its ingredients: Jost solutions, the Gelfand-Levitan equation, the tau function, corresponds to regular vessels, defined by bounded operators. A contribution of this work is the construction of models of vessels corresponding to unbounded operators, which is a first step for the inverse scattering for a wider class of potentials. A detailed research of Jost solutions and the corresponding vessel is presented for the unbounded Sturm-Liouville case. Models of vessels on curves, corresponding to unbounded operators are presented as a tool to study Linear Differential equations of finite order with a spectral parameter and as examples, we show how the family of Non Linear Schrodinger equations and Canonical Systems arise.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-08-23T15:06:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34A30",
      "34A55",
      "46C20",
      "G.1.7",
      "G.1.9",
      "J.2"
    ],
    "keywords": [
      "jost solutions",
      "study linear differential equations",
      "non linear schrodinger equations",
      "sturm-liouville differential equation",
      "unbounded operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.2392M"
    }
  }
}