Lattice equations arising from discrete Painlevé systems. II. $A_4^{(1)}$ case

Nalini Joshi, Nobutaka Nakazono, Yang Shi

In this paper, we construct two lattices from the $\tau$ functions of $A_4^{(1)}$-surface $q$-Painlevé equations, on which quad-equations of ABS type appear. Moreover, using the reduc…