Third-order integrable difference equations generated by a pair of second-order equations
Third-order integrable difference equations generated by a pair of second-order equations
We show that the third-order difference equations proposed by Hirota, Kimura and Yahagi are generated by a pair of second-order difference equations. In some cases, the pair of the second-order equations are equivalent to the Quispel–Robert–Thomson (QRT) system, but in the other cases, they are irrelevant to the QRT system. …