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From integrable equations to Laurent recurrences by Hamad, Khaled; van der Kamp, Peter H is a scholarly article available to read on EtoBox.

What is From integrable equations to Laurent recurrences about?

Based on a recursive factorisation technique we show how integrable difference equations give rise to recurrences which possess the Laurent property. We derive non-autonomous Somos-$k$ sequences, with $k=4,5$, whose coefficients are periodic functions with period 8 for $k=4$, and period 7 for $k=5$, and which possess the Laurent property. We also apply our method to the DTKQ-$N$ equation, with $N=2,3$, and derive Laurent recurrences with $N+2$ terms, of order $N+3$. In the case $N=3$ the recurrence has periodic coefficients with period 8. We demonstrate that recursive factorisation also provides a proof of the Laurent property.

Author

Hamad, Khaled; van der Kamp, Peter H

Published

2014

Language

EN