{
  "id": "math-ph/0509048",
  "version": "v2",
  "published": "2005-09-21T20:58:50.000Z",
  "updated": "2006-11-26T07:15:57.000Z",
  "title": "Reduction and Exact Solutions of the Ideal Magnetohydrodynamic Equations",
  "authors": [
    "Philippe Picard"
  ],
  "comment": "Work-in-progress of some exact solutions of the ideal MHD solutions. We use an analytical method to obtain several particular solutions of this quasilinear and hyperbolic system of PDEs",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper we use the symmetry reduction method to obtain invariant solutions of the ideal magnetohydrodynamic equations in (3+1) dimensions. These equations are invariant under a Galilean-similitude Lie algebra for which the classification by conjugacy classes of r-dimensional subalgebras ($1\\leq r\\leq 4$) was already known. So we restrict our study to the three-dimensional Galilean-similitude subalgebras that give systems composed of ordinary differential equations. We present here several examples of these solutions. Some of these exact solutions show interesting physical interpretations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-11-26T07:15:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76W05",
      "76M60",
      "35C05",
      "35N10"
    ],
    "keywords": [
      "ideal magnetohydrodynamic equations",
      "exact solutions",
      "galilean-similitude lie algebra",
      "symmetry reduction method",
      "three-dimensional galilean-similitude subalgebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.ph...9048P"
    }
  }
}