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Journal of Physics A: Mathematical and Theoretical Volume 41 Number 33 Create an alert RSS this journal

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

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Chris M Field1, Nalini Joshi2 and Frank W Nijhoff3

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Abstract References Cited By
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Bobenko A and Suris Y 2002 Integrable systems on quad-graphs Int. Math. Res. Not. 11 573-611
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Field C M, Joshi N and Nijhoff F W in preparation

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Grammaticos B, Nijhoff F W and Ramani A 1999 Discrete Painlevé equations The Painlevé Property: One Century Later ed R Conte (New York: Springer) pp 413-516
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Garnier R 1912 Sur des équations différentielles du troisième ordre dont l'intégrale générale est uniforme et sur une classe d'équations nouvelles d'ordre supérieur Ann. Écol. Norm. Sup. 29 1-126

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Grammaticos B and Ramani A 2004 Discrete Painlevé equations: a review Discrete Integrable Systems (Lect. Notes Phys. vol 644) ed B Grammaticos, Y Kossmann-Schwarzbach and T Tamizhmani (New York: Springer) pp 245-321

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Hay M, Hietarinta J, Joshi N and Nijhoff F W 2007 A Lax pair for a lattice modified KdV equation, reductions to q-Painlevé equations and associated Lax pairs J. Phys. A: Math. Theor. 40 F61-F73
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Hirota R 1977 Nonlinear partial difference equations: I. A difference analogue of the Korteweg-de Vries equation J. Phys. Soc. Japan 43 1424-33
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Hydon P and Rasin O 2007 Symmetries of integrable difference equations on the quad-graph Stud. Appl. Math. 119 253-69
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Jimbo M and Sakai H 1996 A q-analog of the sixth Painlevé equation Lett. Math. Phys. 38 145-54
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Kajiwara K, Noumi M and Yamada Y 2001 A study on the fourth q-Painlevé equation J. Phys. A: Math. Gen. 34 8563-81
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Kajiwara K, Noumi M and Yamada Y 2002 Discrete dynamical systems with W(A(1)m−1 × A(1)n−1) symmetry Lett. Math. Phys. 60 211-9
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Kajiwara K, Noumi M and Yamada Y 2002 q-Painlevé systems arising from q-KP hierarchy Lett. Math. Phys. 62 259-68
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Nijhoff F W 1996 On some ‘Schwarzian’ equations and their discrete analogues Algebraic Aspects of Integrable Systems: In Memory of Irene Dorfman ed A S Fokas and I M Gel'fand (Basle: Birkhäuser) pp 237-60

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Nijhoff F W 1999 Discrete Painlevé equations and symmetry reduction on the lattice Discrete Integrable geometry and Physics ed A I bobenko and R Seiler (Oxford: Oxford University Press) pp 209-43

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Nijhoff F W and Papageorgiou V G 1991 Similarity reductions of integrable lattices and discrete analogues of the Painlevé II equation Phys. Lett. A 153 337-44
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Nijhoff F W, Quispel G R W and Capel H W 1983 Direct linearization of nonlinear difference-difference equations Phys. Lett. A 97 125-8
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Nijhoff F W, Ramani A, Grammaticos B and Ohta Y 2001 On discrete Painlevé equations associated with the lattice KdV systems and the Painlevé VI equation Stud. Appl. Math. 106 261-314
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Nijhoff F W and Walker A J 2001 The discrete and continuous Painlevé VI hierarchy and the Garnier systems Glasgow Math. J. 43A 109-23
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Papageorgiou V G, Nijhoff F W, Grammaticos B and Ramani A 1992 Isomonodromic deformation problems for discrete analogues of Painlevé equations Phys. Lett. A 164 57-64
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Ramani A and Grammaticos B 2005 On the discrete form of the Fokas-Ablowitz equation Chaos Solitons Fractals 24 1331-5
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Ramani A, Grammaticos B and Hietarinta J 1991 Discrete versions of the Painlevé equations Phys. Rev. Lett. 67 1829-32
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Sahadevan R and Capel H W 2003 Complete integrability and confinement of nonautonomous modified Korteweg-de Vries and sine Gordon mappings Physica A 330 373-90
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Sakai H 2006 Lax form of the q-Painlevé equation associated with the A(1)2 surface J. Phys. A: Math. Gen. 39 12203-10
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