Lagrangian multiform structure for the lattice KP system

Abstract

We present a Lagrangian for the bilinear discrete KP (or Hirota–Miwa) equation. Furthermore, we show that this Lagrangian can be extended to a Lagrangian 3-form when embedded in a higher dimensional lattice, obeying a closure relation. Thus we establish the multiform structure as proposed in Lobb and Nijhoff (2009 J. Phys. A: Math. Theor. 42 454013) in a higher dimensional case.