From integrable equations to Laurent recurrences

الأصل · EN

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.