Lax pairs of discrete Painlevé equations: $(A_2+A_1{)}^{(1)}$ case

Abstract

In this paper, we provide a comprehensive method for constructing Lax pairs of discrete Painlevé equations by using a reduced hypercube structure. In particular, we consider the $A_5^{(1)}$-surface $q$-Painlevé system which has the affine Weyl group symmetry of type $(A_2+A_1{)}^{(1)}$. Two new Lax pairs are found.

13 pages, 2 figures

References in corpus (14)

• On the Linearization of the Painleve' III-VI Equations and Reductions of the Three-Wave Resonant System
• 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
• On the Linearization of the First and Second Painleve' Equations
• Geometry of an elliptic-difference equation related to Q4
• Lattice equations arising from discrete Painlevé systems (I): $(A_2+A_1{)}^{(1)}$ and $(A_1+A_1^{\prime }{)}^{(1)}$ cases
• Geometric Reductions of ABS equations on an $n$-cube to discrete Painlevé systems
• Construction of a Lax Pair for the $E_6^{(1)}$ $q$-Painlevé System
• Lax formalism for q-Painleve equations with affine Weyl group symmetry of type E^{(1)}_n
• Semi-classical Orthogonal Polynomial Systems on Non-uniform Lattices, Deformations of the Askey Table and Analogs of Isomonodromy
• The Padé interpolation method applied to $q$-Painlevé equations
• Lattice equations arising from discrete Painlevé systems. II. $A_4^{(1)}$ case
• Reflection groups and discrete integrable systems

Cited by in corpus (4)

• Lattice equations arising from discrete Painlevé systems (I): $(A_2+A_1{)}^{(1)}$ and $(A_1+A_1^{\prime }{)}^{(1)}$ cases
• Reflection groups and discrete integrable systems
• Hypergeometric $\tau$ Functions of the $q$-Painlevé Systems of Types $A_4^{(1)}$ and $(A_1+A_1^{\prime }{)}^{(1)}$
• On symmetric solutions of the fourth $q$-Painlevé equation