{
  "id": "1405.4947",
  "version": "v1",
  "published": "2014-05-20T04:23:06.000Z",
  "updated": "2014-05-20T04:23:06.000Z",
  "title": "Self-adjointness and conservation laws of difference equations",
  "authors": [
    "Linyu Peng"
  ],
  "comment": "16 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "A general theorem on conservation laws for arbitrary difference equations is proved. The theorem is based on an introduction of an adjoint system related with a given difference system, and it does not require the existence of a difference Lagrangian. It is proved that the system, combined by the original system and its adjoint system, is governed by a variational principle, which inherits all symmetries of the original system. Noether's theorem can then be applied. With some special techniques, e.g. self-adjointness properties, this allows us to obtain conservation laws for difference equations, which are not necessary governed by Lagrangian formalisms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-20T04:23:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conservation laws",
      "adjoint system",
      "original system",
      "arbitrary difference equations",
      "difference system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.4947P"
    }
  }
}