Duality for discrete integrable systems II
Exactly Solvable and Integrable Systems
2018-08-15 v2
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.
Keywords
Cite
@article{arxiv.1711.05886,
title = {Duality for discrete integrable systems II},
author = {Peter H. van der Kamp and G. R. W Quispel and Da-jun Zhang},
journal= {arXiv preprint arXiv:1711.05886},
year = {2018}
}
Comments
11 pages, 2 figures