{
  "id": "2402.03788",
  "version": "v1",
  "published": "2024-02-06T08:08:34.000Z",
  "updated": "2024-02-06T08:08:34.000Z",
  "title": "Symmetry reductions of a generalized Kuramoto-Sivashinsky equation via equivalence transformations",
  "authors": [
    "Rafael de la Rosa",
    "María de los Santos Bruzón"
  ],
  "comment": "18 pages",
  "journal": "Communications in Nonlinear Science and Numerical Simulation, 63:12-20, 2018",
  "doi": "10.1016/j.cnsns.2018.02.038",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we consider a generalized Kuramoto-Sivashinsky equation. The equivalence group of the class under consideration has been constructed. This group allows us to perform a comprehensive study and a clear and concise formulation of the results. We have constructed the optimal system of subalgebras of the projections of the equivalence algebra on the space formed by the dependent variable and the arbitrary functions. By using this optimal system, all nonequivalent equations admitting an extension by one of the principal Lie algebra of the class under consideration can be determined. Taking into account the additional symmetries obtained we reduce some partial differential equations belonging to the class into ordinary differential equations. We derive some exact solutions of these equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-02-06T08:08:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generalized kuramoto-sivashinsky equation",
      "equivalence transformations",
      "symmetry reductions",
      "optimal system",
      "principal lie algebra"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}