{
  "id": "1409.6091",
  "version": "v1",
  "published": "2014-09-22T07:05:20.000Z",
  "updated": "2014-09-22T07:05:20.000Z",
  "title": "A new technique for finding conservation laws of partial differential equations",
  "authors": [
    "Zhi-Yong Zhang"
  ],
  "categories": [
    "math-ph",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "We propose a new technique to construct conservation laws of partial differential equations (PDEs), where the whole computations can be fully implemented on a computer. The result is obtained by proving that any adjoint symmetry of PDEs is a differential substitution of nonlinear self-adjointness and vice versa. Consequently, each symmetry of PDEs corresponds to a conservation law via a formula if the PDEs are nonlinearly self-adjoint with differential substitution, which extends the results of Noether' theorem. As a byproduct, we find that the set of differential substitutions includes the set of conservation law multipliers as a subset. With the help of the computer algebra system Mathematica, applications to the illustrated examples are performed and new conservation laws are constructed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-22T07:05:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "partial differential equations",
      "finding conservation laws",
      "differential substitution",
      "computer algebra system mathematica",
      "conservation law multipliers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}