### Abstract

This paper mainly contributes to the extension of Noether's theorem to differential-difference equations. For this purpose, we first investigate the prolongation formula for continuous symmetries, which makes a characteristic representation possible. The relations of symmetries, conservation laws, and the Fréchet derivative are also investigated. For nonvariational equations, because Noether's theorem is now available, the self-adjointness method is adapted to the computation of conservation laws for differential-difference equations. Several differential-difference equations are investigated as illustrative examples, including the Toda lattice and semidiscretizations of the Korteweg–de Vries (KdV) equation. In particular, the Volterra equation is taken as a running example.

Original language | English |
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Pages (from-to) | 457-502 |

Number of pages | 46 |

Journal | Studies in Applied Mathematics |

Volume | 139 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2017 Oct |

Externally published | Yes |

### ASJC Scopus subject areas

- Applied Mathematics