Duality for discrete integrable systems II

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.