Self-adjointness and conservation laws of difference equations

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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
Issue number1-3
Publication statusPublished - 2015 Jun 1
Externally publishedYes


  • Conservation laws
  • Noether's theorem
  • Symmetries

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics


Dive into the research topics of 'Self-adjointness and conservation laws of difference equations'. Together they form a unique fingerprint.

Cite this