Geodesic
An integrable multicomponent quad-equation and its Lagrangian formulation
Teoretičeskaâ i matematičeskaâ fizika, Tome 173 (2012) no. 3, pp. 363-374

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We present a hierarchy of discrete systems whose first members are the lattice modified Korteweg–de Vries equation and the lattice modified Boussinesq equation. The $N$th member in the hierarchy is an $N$-component system defined on an elementary plaquette in the two-dimensional lattice. The system is multidimensionally consistent, and we obtain a Lagrangian that respects this feature, i.e., has the desirable closure property.
Keywords: integrable system, discrete equation, reduction, variational principle.
Mots-clés : Lagrange formulation 
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     title = {An integrable multicomponent quad-equation and its {Lagrangian} formulation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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J. Atkinson; S. B. Lobb; F. W. Nijhoff. An integrable multicomponent quad-equation and its Lagrangian formulation. Teoretičeskaâ i matematičeskaâ fizika, Tome 173 (2012) no. 3, pp. 363-374. http://geodesic.mathdoc.fr/item/TMF_2012_173_3_a1/