{
  "id": "1105.5303",
  "version": "v4",
  "published": "2011-05-26T14:26:27.000Z",
  "updated": "2013-08-02T08:17:14.000Z",
  "title": "Exact Solutions of Nonlinear Partial Differential Equations by the Method of Group Foliation Reduction",
  "authors": [
    "Stephen C. Anco",
    "Sajid Ali",
    "Thomas Wolf"
  ],
  "comment": "Typos in the solutions are corrected",
  "journal": "SIGMA 7 (2011), 066, 11 pages",
  "doi": "10.3842/SIGMA.2011.066",
  "categories": [
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "A novel symmetry method for finding exact solutions to nonlinear PDEs is illustrated by applying it to a semilinear reaction-diffusion equation in multi-dimensions. The method uses a separation ansatz to solve an equivalent first-order group foliation system whose independent and dependent variables respectively consist of the invariants and differential invariants of a given one-dimensional group of point symmetries for the reaction-diffusion equation. With this group-foliation reduction method, solutions of the reaction-diffusion equation are obtained in an explicit form, including group-invariant similarity solutions and travelling-wave solutions, as well as dynamically interesting solutions that are not invariant under any of the point symmetries admitted by this equation.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-08-02T08:17:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear partial differential equations",
      "group foliation reduction",
      "exact solutions",
      "reaction-diffusion equation",
      "equivalent first-order group foliation system"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "SIGMA",
      "year": 2011,
      "month": "Jul",
      "volume": 7,
      "pages": "066"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011SIGMA...7..066A"
    }
  }
}