Transformations, symmetries and Noether theorems for differential-difference equations

Linyu Peng, Peter E. Hydon

研究成果: Article査読

抄録

The first part of this paper develops a geometric setting for differential-difference equations that resolves an open question about the extent to which continuous symmetries can depend on discrete independent variables. For general mappings, differentiation and differencing fail to commute. We prove that there is no such failure for structure-preserving mappings, and identify a class of equations that allow greater freedom than is typical. For variational symmetries, the above results lead to a simple proof of the differential-difference version of Noether's theorem. We state and prove the differential-difference version of Noether's second theorem, together with a Noether-type theorem that spans the gap between the analogues of Noether's two theorems. These results are applied to various equations from physics.

本文言語English
論文番号20210944
ジャーナルProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
478
2259
DOI
出版ステータスPublished - 2022

ASJC Scopus subject areas

  • 数学 (全般)
  • 工学(全般)
  • 物理学および天文学(全般)

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