An integrable multicomponent quad equation and its Lagrangian formulation

TL;DR

This paper introduces a hierarchy of integrable multicomponent discrete systems, including the lattice modified KdV and Boussinesq equations, with a focus on their multidimensional consistency and Lagrangian formulation.

Contribution

It presents a new hierarchy of multidimensionally consistent multicomponent lattice equations with an associated Lagrangian that satisfies the closure property.

Findings

Hierarchy includes lattice modified KdV and Boussinesq equations

Systems are multidimensionally consistent

A Lagrangian with closure property is constructed

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.