Multiplicative equations related to the affine Weyl group E_{8}
Abstract
We derive integrable equations starting from autonomous mappings with a general form inspired by the multiplicative systems associated with the affine Weyl group E_{8}^{(1 )}. Five such systems are obtained, three of which turn out to be linearisable and the remaining two are integrable in terms of elliptic functions. In the case of the linearisable mappings, we derive nonautonomous forms which contain a free function of the independent variable and we present the linearisation in each case. The two remaining systems are deautonomised to new discrete Painlevé equations. We show that these equations are in fact special forms of much richer systems associated with the affine Weyl groups E_{7}^{(1 )} and E_{8}^{(1 )}, respectively.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 August 2017
 DOI:
 10.1063/1.4997166
 arXiv:
 arXiv:1705.01679
 Bibcode:
 2017JMP....58h3502G
 Keywords:

 Mathematical Physics;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 9 pages, no figures