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Journal of Nonlinear Mathematical Physics Volume 12, 2005 - Issue sup1: Special Issue in Honour of Francesco Calogero on the Occasion of His 70th Birthday
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Original Articles

Reductions of Integrable Lattices

B Grammaticos GMPIB, Université Paris VII, case 7021, 75251, Paris E-mail: [email protected]
,
A Ramani Ecole Polytechnique, CNRS, UMR 7644, 91128, Palaiseau, France E-mail: [email protected]
,
J Satsuma Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, 153-8914, Meguro-ku, Tokyo, Japan
,
R Willox Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, 153-8914, Meguro-ku, Tokyo, Japan
&
A S Carstea Institute of Physics and Nuclear Engineering, Magurele, Bucharest, Romania
Pages 363-371 | Published online: 21 Jan 2013

Citations (24)

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Huda Alrashdi, Nalini Joshi & Dinh Thi Tran. (2020) Hierarchies of q-discrete Painlevé equations. Journal of Nonlinear Mathematical Physics 27:3, pages 453-477.
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Articles from other publishers (23)

A. S. Carstea & T. Takenawa. (2019) Super-QRT and 4D-mappings reduced from the lattice super-KdV equation. Journal of Mathematical Physics 60:9.
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Gino Biondini & Qiao Wang. (2018) Discrete and continuous coupled nonlinear integrable systems via the dressing method. Studies in Applied Mathematics 142:2, pages 139-161.
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Pavlos Xenitidis. (2018) Deautonomizations of integrable equations and their reductions. Journal of Integrable Systems 3:1.
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Nobutaka Nakazono, Yang Shi & Masataka Kanki. 2017. Symmetries and Integrability of Difference Equations. Symmetries and Integrability of Difference Equations 1 41 .
Nalini Joshi, Nobutaka Nakazono & Yang Shi. (2016) Lattice equations arising from discrete Painlevé systems: II. ${A}_{4}^{(1)}$ case. Journal of Physics A: Mathematical and Theoretical 49:49, pages 495201.
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Nalini Joshi & Nobutaka Nakazono. (2016) Lax pairs of discrete Painlevé equations: ( A 2 + A 1 ) (1) case . Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472:2196, pages 20160696.
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Nalini Joshi, Nobutaka Nakazono & Yang Shi. (2015) Lattice equations arising from discrete Painlevé systems. I. ( A 2 + A 1)(1) and (A1+A1′)(1) cases . Journal of Mathematical Physics 56:9.
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Mike Hay, Phil Howes, Nobutaka Nakazono & Yang Shi. (2015) A systematic approach to reductions of type-Q ABS equations. Journal of Physics A: Mathematical and Theoretical 48:9, pages 095201.
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N Joshi, N Nakazono & Y Shi. (2014) Geometric reductions of ABS equations on an n -cube to discrete Painlevé systems . Journal of Physics A: Mathematical and Theoretical 47:50, pages 505201.
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Christopher M Ormerod, Peter H van der Kamp, Jarmo Hietarinta & G R W Quispel. (2014) Twisted reductions of integrable lattice equations, and their Lax representations. Nonlinearity 27:6, pages 1367-1390.
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Adam Doliwa. (2014) Non-commutative q -Painlev? VI equation . Journal of Physics A: Mathematical and Theoretical 47:3, pages 035203.
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Corina Babalic & Adrian Carstea. (2014) On some new forms of lattice integrable equations. Open Physics 12:5.
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Adam Doliwa. (2013) Non-commutative lattice-modified Gel’fand–Dikii systems. Journal of Physics A: Mathematical and Theoretical 46:20, pages 205202.
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C M Ormerod, Peter H van der Kamp & G R W Quispel. (2013) Discrete Painlevé equations and their Lax pairs as reductions of integrable lattice equations. Journal of Physics A: Mathematical and Theoretical 46:9, pages 095204.
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Christopher M. Ormerod. (2012) Reductions of lattice mKdV to q- . Physics Letters A 376:45, pages 2855-2859.
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C Scimiterna, B Grammaticos & A Ramani. (2011) On two integrable lattice equations and their interpretation. Journal of Physics A: Mathematical and Theoretical 44:3, pages 032002.
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Mike Hay. (2009) A completeness study on discrete, 2×2 Lax pairs. Journal of Mathematical Physics 50:10.
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Chris M Field, Nalini Joshi & Frank W Nijhoff. (2008) q -difference equations of KdV type and Chazy-type second-degree difference equations . Journal of Physics A: Mathematical and Theoretical 41:33, pages 332005.
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Olexandr G Rasin & Peter E Hydon. (2007) Conservation laws for integrable difference equations. Journal of Physics A: Mathematical and Theoretical 40:42, pages 12763-12773.
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Mike Hay. (2007) Hierarchies of nonlinear integrable q -difference equations from series of Lax pairs . Journal of Physics A: Mathematical and Theoretical 40:34, pages 10457-10471.
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R. Sahadevan, O.G. Rasin & P.E. Hydon. (2007) Integrability conditions for nonautonomous quad-graph equations. Journal of Mathematical Analysis and Applications 331:1, pages 712-726.
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Mike Hay, Jarmo Hietarinta, Nalini Joshi & Frank Nijhoff. (2007) A Lax pair for a lattice modified KdV equation, reductions to q -Painlevé equations and associated Lax pairs . Journal of Physics A: Mathematical and Theoretical 40:2, pages F61-F73.
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N. Joshi, B. Grammaticos, T. Tamizhmani & A. Ramani. (2006) From Integrable Lattices to Non-QRT Mappings. Letters in Mathematical Physics 78:1, pages 27-37.
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