Relations between symmetries and conservation laws for difference systems

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2 Citations (Scopus)


This paper presents a relation between divergence variational symmetries for difference variational problems on lattices and conservation laws for the associated Euler–Lagrange system provided by Noether's theorem. This inspires us to define conservation laws related to symmetries for arbitrary difference equations with or without Lagrangian formulations. These conservation laws are constrained by partial differential equations obtained from the symmetries generators. It is shown that the orders of these partial differential equations have been reduced relative to those used in a general approach. Illustrative examples are presented.

Original languageEnglish
Pages (from-to)1609-1626
Number of pages18
JournalJournal of Difference Equations and Applications
Issue number12
Publication statusPublished - 2014 Dec 2
Externally publishedYes


  • conservation law
  • difference equation
  • difference variational problem
  • symmetry

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics


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