A novel nth order difference equation that may be integrable

Dmitry Demskoy, D.T. Tran, P.H. van der Kamp, G.R.W. Quispel

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

We derive an nth order difference equation as a dual of a very simple periodic equation, and construct (n + 1)/2 explicit integrals and integrating factors of this equation in terms of multi-sums of products. We also present a generating function for the degrees of its iterates, exhibiting polynomial growth. In conclusion we demonstrate how the equation in question arises as a reduction of a system of lattice equations related to an integrable equation of Levi and Yamilov. These three facts combine to suggest the integrability of the nth order difference equation.
Original languageEnglish
Pages (from-to)1-12
Number of pages12
JournalJournal of Physics A: Mathematical and Theoretical
Volume45
Issue number13
DOIs
Publication statusPublished - Apr 2012

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