On the Lagrangian Structure of Integrable Quad-Equations

  title={On the Lagrangian Structure of Integrable Quad-Equations},
  author={Alexander I. Bobenko and Yuri B. Suris},
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… CONTINUE READING

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Lagrangian multiform structure for the lattice KP system

  • S. B. Lobb, F. W. Nijhoff, Quispel G.R.W.
  • J. Phys. A: Math. Theor. 42(47), paper id. 472002…
  • 2009
1 Excerpt

Discrete differential geometry: integrable structures

  • A. I. Bobenko, Suris, Yu.B.
  • Graduate Studies in Mathematics, vol. 98…
  • 2008
1 Excerpt

Discrete Lagrangian models

  • Suris, Yu.B.
  • Grammaticos, B., KosmannSchwarzbach, Y…
  • 2004
1 Excerpt

Q4: integrable master equation related to an elliptic curve

  • V. E. Adler, Suris, Yu.B.
  • Int. Math. Res. Notice 47, 2523–2553
  • 2004
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