Affine Lie algebras, Lax pairs and integrable discrete and continuous   systems
  A consistent set of six integrable discrete and continuous dynamical systems are suggested corresponding to arbitrary affine Lie algebra. The set contains a system of partial differential equations which can be treated as a version of generalized Toda lattice while semi-discrete systems in the set define the Backlund transform for this Toda lattice and the fully discrete representative of the set can be obtained as a superposition of such kind Backlund transforms. Four linear Zakharov-Shabat type systems taken pairwise realize Lax pairs for these six dynamical systems. 
Rustem N. Garifullin and Ismagil T. Habibullin
nlin.SI