Lagrangian multiform structure for the lattice KP system

TL;DR

This paper introduces a Lagrangian formulation for the discrete KP system and extends it to a multiform structure in higher dimensions, demonstrating a closure relation that generalizes previous theoretical frameworks.

Contribution

It provides the first Lagrangian 3-form for the lattice KP system, establishing a multiform structure in higher dimensions and confirming the closure relation.

Findings

Lagrangian for bilinear discrete KP equation derived

Extension to a Lagrangian 3-form in higher dimensions shown

Multiform structure obeying closure relation established

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 arXiv:0903.4086v1 [nlin.SI] in a higher dimensional case.