We study the variational structure of the discrete Kadomtsev-Petviashvili (dKP) equation by means of its pluri-Lagrangian formulation. We consider the dKP equation and its variational formulation on the cubic lattice ${ \mathbb Z}^{ N}$ as well as on the root lattice $Q(A_{ N})$. We prove that, on a lattice of dimension at least four, the corresponding Euler-Lagrange equations are equivalent to the dKP equation.
Categories: math-ph math.MP math.SG nlin.SI