A novel nth order difference equation that may be integrable

作者：Demskoi D K^*; Tran D T; van der Kamp P H; Quispel G R W

来源：Journal of Physics A-Mathematical and Theoretical, 2012, 45(13): 135202.

DOI：10.1088/1751-8113/45/13/135202

We derive an nth order difference equation as a dual of a very simple periodic equation, and construct lfloor(n+1)/2rfloor 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.

• 出版日期2012-4-6