{
  "id": "2108.02171",
  "version": "v1",
  "published": "2021-08-02T10:01:52.000Z",
  "updated": "2021-08-02T10:01:52.000Z",
  "title": "Lie remarkable partial differential equations characterized by Lie algebras of point symmetries",
  "authors": [
    "Matteo Gorgone",
    "Francesco Oliveri"
  ],
  "comment": "22 pages",
  "journal": "J. Geom. Phys. 144, 314--323 (2019)",
  "doi": "10.1016/j.geomphys.2019.06.011",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Within the framework of inverse Lie problem, we give some non-trivial examples of coupled Lie remarkable equations, \\textit{i.e.}, classes of differential equations that are in correspondence with their Lie point symmetries. In particular, we determine hierarchies of second order partial differential equations uniquely characterized by affine transformations of $\\mathbb{R}^{n+m}$, and a system of two third order partial differential equations in two independent variables uniquely determined by the Lie algebra of projective transformations of $\\mathbb{R}^4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-02T10:01:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lie algebra",
      "third order partial differential equations",
      "second order partial differential equations",
      "inverse lie problem",
      "lie point symmetries"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}