Self-Dual Systems, their Symmetries and Reductions to the Bogoyavlensky Lattice

[摘要] We recently introduced a class of ${\mathbb{Z}}_N$ graded discrete Lax pairs and studied the associated discrete integrable systems (lattice equations). In particular, we introduced a subclass, which we called ''self-dual''. In this paper we discuss the continuous symmetries of these systems, their reductions and the relation of the latter to the Bogoyavlensky equation.

[关键词] discrete integrable system;Lax pair;symmetry;Bogoyavlensky system