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.
|Number of pages||12|
|Journal||Journal of Physics A: Mathematical and Theoretical|
|Publication status||Published - Apr 2012|
Demskoy, D., Tran, D. T., van der Kamp, P. H., & Quispel, G. R. W. (2012). A novel nth order difference equation that may be integrable. Journal of Physics A: Mathematical and Theoretical, 45(13), 1-12. https://doi.org/10.1088/1751-8113/45/13/135202