An integrable multicomponent quad equation and its Lagrangian formulation
arXiv:1204.5521 · doi:10.1007/s11232-012-0138-y
Abstract
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 2-dimensional lattice. The system is multidimensionally consistent and a Lagrangian which respects this feature, i.e., which has the desirable closure property, is obtained.
10 pages