Third-order integrable difference equations generated by a pair of second-order equations
arXiv:nlin/0512072 · doi:10.1088/0305-4470/39/5/009
Abstract
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. We also discuss an ultradiscretization of the equations.
15 pages, 3 figures; Accepted for Publication in J. Phys. A
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