Self-adjointness and conservation laws of difference equations

Linyu Peng

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)209-219
Number of pages11
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume23
Issue number1-3
DOIs
Publication statusPublished - 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

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