Transactions of the Japan Society for Industrial and Applied Mathematics
Online ISSN : 2424-0982
ISSN-L : 0917-2246
Higher-order integrable difference equations generated from second-order ones(Theory,Applied Integrable Systems,<Special Issue>Joint Symposium of JSIAM Activity Groups 2006)
Hidetomo NagaiDaisuke TakahashiJunta Matsukidaira
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2006 Volume 16 Issue 3 Pages 197-210

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Abstract
A new method to construct a higher-order integrable difference equations generated from second-order ones is proposed. Using this method, we can obtain third or higher-order integrable difference equations from Quispel-Roberts-Thompson(QRT) systems. Moreover, we can obtain third-order integrable equations from discrete Painleve I equations. The higher-order equation can also be separated into a set of second-order integrable equations on separated lattices. Especially, a pair of discrete Painleve II equations on even and odd lattices are obtained via the third-order equation derived from a pair of discrete Painleve I equations.
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© 2006 The Japan Society for Industrial and Applied Mathematics
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