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arXiv · 1603.09414

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

Nalini Joshi·Nobutaka Nakazono·Yang Shi
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Abstract

In this paper, we construct two lattices from the $τ$ functions of $A_4^{(1)}$-surface $q$-Painlevé equations, on which quad-equations of ABS type appear. Moreover, using the reduced hypercube structure, we obtain the Lax pairs of the $A_4^{(1)}$-surface $q$-Painlevé equations.

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Nalini Joshi, Nobutaka Nakazono, Yang Shi. 2016-09-15. Lattice equations arising from discrete Painlevé systems. II. $A_4^{(1)}$ case. https://doi.org/10.1088/1751-8113%2F49%2F49%2F495201

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