Third-order integrable difference equations generated by a pair of second-order equations

Details 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

2005-12-26

arxiv.org/abs/nlin/0512072v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

15 pages, 3 figures; Accepted for Publication in J. Phys. A

Scientific paper

10.1088/0305-4470/39/5/009

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.

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