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

Abstract

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 reduced hypercube structure, we obtain the Lax pairs of the $A_4^{(1)}$-surface $q$-Painlevé equations.

32 pages, 6 figures

References in corpus (8)

• Lax forms of the $q$-Painlevé equations
• q-Difference equations of KdV type and "Chazy-type" second-degree difference equations
• A Lax Formalism for the Elliptic Difference Painlevé Equation
• Hypergeometric $\tau$-Functions of the $q$-Painlevé System of Type $E_7^{(1)}$
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• Construction of a Lax Pair for the $E_6^{(1)}$ $q$-Painlevé System
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Cited by in corpus (3)

• Lax pairs of discrete Painlevé equations: $(A_2+A_1{)}^{(1)}$ case
• Discrete Painlevé transcendent solutions to the multiplicative type discrete KdV equations
• Reduction of lattice equations to the Painlevé equations: P${}_{\mathrm{IV}}$ and P${}_{\mathrm{V}}$