Duality for discrete integrable systems II

TL;DR

This paper extends the concept of duality to lattice equations, introduces a new 3D lattice equation dual to the lattice AKP, and explores its reductions, conservation laws, and conjectured soliton solutions.

Contribution

It generalizes duality to lattice equations and derives a novel 3D lattice equation with various reductions and properties.

Findings

Derived a new 3D lattice equation dual to the lattice AKP.

Connected the new equation to known integrable systems like QD and HADT.

Provided conservation laws and conjectured soliton solutions.

Abstract

We generalise the concept of duality to lattice equations. We derive a novel 3 dimensional lattice equation, which is dual to the lattice AKP equation. Reductions of this equation include Rutishauser's quotient-difference (QD) algorithm, the higher analogue of the discrete time Toda (HADT) equation and its corresponding quotient-quotient-difference (QQD) system, the discrete hungry Lotka-Volterra system, discrete hungry QD, as well as the hungry forms of HADT and QQD. We provide three conservation laws, we conjecture the equation admits N-soliton solutions and that reductions have the Laurent property and vanishing algebraic entropy.