Integrable and superintegrable systems associated with multi-sums of products

Peter H van der Kamp; Theodoros E Kouloukas; G R W Quispel; Dinh T Tran; Pol Vanhaecke

doi:10.1098/rspa.2014.0481

Integrable and superintegrable systems associated with multi-sums of products

Proc Math Phys Eng Sci. 2014 Dec 8;470(2172):20140481. doi: 10.1098/rspa.2014.0481.

Authors

Peter H van der Kamp¹, Theodoros E Kouloukas¹, G R W Quispel¹, Dinh T Tran¹, Pol Vanhaecke²

Affiliations

¹ Department of Mathematics , La Trobe University , Bundoora (Melbourne) Victoria 3086, Australia.
² Laboratoire de Mathématiques et Applications, UMR 7348 du CNRS , Université de Poitiers , 86962 Futuroscope Chasseneuil Cedex, France.

Abstract

We construct and study certain Liouville integrable, superintegrable and non-commutative integrable systems, which are associated with multi-sums of products.

Keywords: Kahan discretization; Lax representation; Lotka–Volterra system; integrable systems; superintegrability.