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Sufficient number of integrals for the pth-order Lyness equation
journal contributionposted on 29.03.2022, 03:37 authored by DT Tran, Pieter Van Der KampPieter Van Der Kamp, Gilles QuispelGilles Quispel
In this communication, we present a sufficient number of first integrals for the Lyness equation of arbitrary order. We first use the staircase method (Quispel et al 1991 Physica A 173 243-66) to construct integrals of a derivative equation of the Lyness equation. Closed-form expressions for the integrals are given based on a non-commutative Vieta expansion. The integrals of the Lyness equation then follow directly from these integrals. Previously found integrals for the Lyness equation arise as special cases of our new set of integrals. © 2010 IOP Publishing Ltd.