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

preprint2016arXivOpen access

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

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Lattice equations arising from discrete Painlevé systems. II. A4(1)A_4^{(1)}A4(1)​ case

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