Chris M Field et al 2008 J. Phys. A: Math. Theor. 41 332005 doi:10.1088/1751-8113/41/33/332005
q-difference equations of KdV type and Chazy-type second-degree difference equations
FREE ARTICLEChris M Field1, Nalini Joshi2 and Frank W Nijhoff3
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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. This second-order second-degree equation follows from a system in terms of two variables from which also follows an associated third-order first-degree equation. We present the isomonodromic deformation problem for the two-variable system and discuss the relation between the hierarchy of second-degree ordinary q-difference equations and other equations of Painlevé type.
- PACS
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05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
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- Dates
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Issue 33 (22 August 2008)
Received 16 May 2008, in final form 25 June 2008
Published 18 July 2008
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q-difference equations of KdV type and Chazy-type second-degree difference equations
Chris M Field et al 2008 J. Phys. A: Math. Theor. 41 332005
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