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arXiv · 1401.7044

Lattice equations arising from discrete Painlev\'e systems (I): $(A_2+A_1)^{(1)}$ and $(A_1+A_1')^{(1)}$ cases

Nalini Joshi·Nobutaka Nakazono·Yang Shi
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Abstract

We introduce the concept of $\omega$-lattice, constructed from $\tau$ functions of Painlev\'e systems, on which quad-equations of ABS type appear. In particular, we consider the $A_5^{(1)}$- and $A_6^{(1)}$-surface $q$-Painlev\'e systems corresponding affine Weyl group symmetries are of $(A_2+A_1)^{(1)}$- and $(A_1+A_1)^{(1)}$-types, respectively.

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Nalini Joshi, Nobutaka Nakazono, Yang Shi. 2014-01-27. Lattice equations arising from discrete Painlev\'e systems (I): $(A_2+A_1)^{(1)}$ and $(A_1+A_1')^{(1)}$ cases. https://doi.org/10.1063/1.4931481

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