{
  "id": "math-ph/0207023",
  "version": "v1",
  "published": "2002-07-18T17:13:05.000Z",
  "updated": "2002-07-18T17:13:05.000Z",
  "title": "A precise definition of reduction of partial differential equations",
  "authors": [
    "Renat Z. Zhdanov",
    "Ivan M. Tsyfra",
    "Roman O. Popovych"
  ],
  "comment": "LaTeX, 21 pages",
  "journal": "J. Math. Anal. Appl. 238 (1999), 101-123",
  "doi": "10.1006/jmaa.1999.6511",
  "categories": [
    "math-ph",
    "math.AP",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "We give a comprehensive analysis of interrelations between the basic concepts of the modern theory of symmetry (classical and non-classical) reductions of partial differential equations. Using the introduced definition of reduction of differential equations we establish equivalence of the non-classical (conditional symmetry) and direct (Ansatz) approaches to reduction of partial differential equations. As an illustration we give an example of non-classical reduction of the nonlinear wave equation in (1+3) dimensions. The conditional symmetry approach when applied to the equation in question yields a number of non-Lie reductions which are far-reaching generalization of the well-known symmetry reductions of the nonlinear wave equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-07-18T17:13:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A30",
      "35L70",
      "58J70"
    ],
    "keywords": [
      "partial differential equations",
      "precise definition",
      "nonlinear wave equation",
      "conditional symmetry approach",
      "well-known symmetry reductions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.ph...7023Z"
    }
  }
}