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Sufficient number of integrals for the pth-order Lyness equation

journal contribution
posted on 2022-03-29, 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.

Funding

This research has been funded by the Australian Research Council through the Centre of Excellence for Mathematics and Statistics of Complex Systems. DTT acknowledges the support of two scholarships, one from La Trobe University and the other from the Endeavour IPRS programme.

History

Publication Date

2010-06-24

Journal

Journal of Physics A: Mathematical and Theoretical

Volume

43

Issue

30

Article Number

302001

Pagination

11p.

Publisher

IOP Publishing

ISSN

1751-8113

Rights Statement

© 2010 IOP Publishing Ltd

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    Keywords

    Lyness equationsufficient number of first integralsclosed-form expressionsnon-commutative Vieta expansion

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