### 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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Journal | Studies in Applied Mathematics |

DOIs | |

Publication status | Accepted/In press - 2017 |

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### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

**Symmetries, Conservation Laws, and Noether's Theorem for Differential-Difference Equations.** / Peng, Linyu.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Symmetries, Conservation Laws, and Noether's Theorem for Differential-Difference Equations

AU - Peng, Linyu

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85017399706&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85017399706&partnerID=8YFLogxK

U2 - 10.1111/sapm.12168

DO - 10.1111/sapm.12168

M3 - Article

AN - SCOPUS:85017399706

JO - Studies in Applied Mathematics

JF - Studies in Applied Mathematics

SN - 0022-2526

ER -