q-Difference equations of KdV type and "Chazy-type" second-degree difference equations

Abstract

By imposing special compatible similarity constraints on a class of integrable partial $q$-difference equations of KdV-type we derive a hierarchy of second-degree ordinary $q$-difference equations. The lowest (non-trivial) member of this hierarchy is a second-order second-degree equation which can be considered as an analogue of equations in the class studied by Chazy. We present corresponding isomonodromic deformation problems and discuss the relation between this class of difference equations and other equations of Painleve type.

14 pages, 2 figures

References in corpus (2)

• A $q$-anaolg of the sixth Painlevé equation
• A study on the fourth q-Painlevé equation

Cited by in corpus (5)

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• Geometric Reductions of ABS equations on an $n$-cube to discrete Painlevé systems
• Lattice equations arising from discrete Painlevé systems (I): $(A_2+A_1{)}^{(1)}$ and $(A_1+A_1^{\prime }{)}^{(1)}$ cases
• Lax pairs of discrete Painlevé equations: $(A_2+A_1{)}^{(1)}$ case
• Lattice equations arising from discrete Painlevé systems. II. $A_4^{(1)}$ case