On the Lagrangian structure of Integrable quad-equations

Alexander I. Bobenko, Yuri B. Suris

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


The new idea of flip invariance of action functionals in multidimensional lattices was recently highlighted as a key feature of discrete integrable systems. Flip invariance was proved for several particular cases of integrable quad-equations by Bazhanov, Mangazeev and Sergeev and by Lobb and Nijhoff. We provide a simple and case-independent proof for all integrable quad-equations. Moreover, we find a new relation for Lagrangians within one elementary quadrilateral which seems to be a fundamental building block of the various versions of flip invariance.

Original languageEnglish
Pages (from-to)17-31
Number of pages15
JournalLetters in Mathematical Physics
Issue number1
StatePublished - Mar 2010
Externally publishedYes


  • ABS list
  • Discrete Lagrangian multiforms
  • Flip invariance of the action
  • Integrable quad-equations
  • Star-triangle relation


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