2006 年 16 巻 3 号 p. 197-210
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.