{
  "id": "2407.06381",
  "version": "v1",
  "published": "2024-07-08T20:49:03.000Z",
  "updated": "2024-07-08T20:49:03.000Z",
  "title": "Hierarchy of coupled Burgers-like equations induced by conditional symmetries",
  "authors": [
    "M. Gorgone",
    "F. Oliveri",
    "E. Sgroi"
  ],
  "comment": "27 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "It is known that $Q$-conditional symmetries of the classical Burgers' equation express in terms of three functions satisfying a coupled system of Burgers-like equations. The search of conditional symmetries of this system leads to a system of five coupled Burgers-like equations. Iterating the procedure, an infinite hierarchy of systems made of an odd number of coupled Burgers-like equations is obtained. Moreover, starting from a pair of Burgers-like equations, a similar hierarchy of systems made of an even number of coupled Burgers-like equations arises; it is also proved that the two hierarchies may be unified. Writing a generic element of this hierarchy as a matrix Burgers' equation, the existence of the matrix Hopf-Cole transformation allows for its linearization and the determination of its solution. Finally, it is shown that each element of the hierarchy possesses a five-dimensional Lie algebra of classical point symmetries. Though these Lie algebras are realized in manifolds with different dimensionality, they are all isomorphic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-08T20:49:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K10",
      "58J70",
      "58J72"
    ],
    "keywords": [
      "conditional symmetries",
      "matrix hopf-cole transformation",
      "five-dimensional lie algebra",
      "similar hierarchy",
      "coupled burgers-like equations arises"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}