Sufficient number of integrals for thepth-order Lyness equation
Dinh T Tran, Peter H. van der Kamp, Gilles Quispel · Journal of Physics A Mathematical and Theoretical · 2010
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.