{
  "id": "1610.01029",
  "version": "v1",
  "published": "2016-10-04T14:53:42.000Z",
  "updated": "2016-10-04T14:53:42.000Z",
  "title": "Supersymmetric versions of the Fokas-Gel'fand formula for immersion",
  "authors": [
    "S. Bertrand",
    "A. M. Grundland"
  ],
  "comment": "23 pages",
  "journal": "J. Phys. A: Math. Theor.49, 30, 305201 (2016)",
  "doi": "10.1088/1751-8113/49/30/305201",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper, we construct and investigate two supersymmetric versions of the Fokas-Gel'fand formula for the immersion of 2D surfaces associated with a supersymmetric integrable system. The first version involves an infinitesimal deformation of the zero-curvature condition and the linear spectral problem associated with this system. This deformation leads the surfaces to be represented in terms of a bosonic supermatrix immersed in a Lie superalgebra. The second supersymmetric version is obtained by using a fermionic parameter deformation to construct surfaces expressed in terms of a fermionic supermatrix immersed in a Lie superalgebra. For both extensions, we provide a geometrical characterization of deformed surfaces using the super Killing form as an inner product and a super moving frame formalism. The theoretical results are applied to the supersymmetric sine-Gordon equation in order to construct super soliton surfaces associated with five different symmetries. We find integrated forms of these surfaces which represent constant Gaussian curvature surfaces and nonlinear Weingarten-type surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-04T14:53:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q51",
      "53A05",
      "22E70"
    ],
    "keywords": [
      "fokas-gelfand formula",
      "represent constant gaussian curvature surfaces",
      "construct super soliton surfaces",
      "lie superalgebra",
      "nonlinear weingarten-type surfaces"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "IOP"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}