### 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.

Original language | English |
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Pages (from-to) | 209-219 |

Number of pages | 11 |

Journal | Communications in Nonlinear Science and Numerical Simulation |

Volume | 23 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 2015 Jun 1 |

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### Keywords

- Conservation laws
- Noether's theorem
- Symmetries

### ASJC Scopus subject areas

- Modelling and Simulation
- Numerical Analysis
- Applied Mathematics