Integrable equations and recursion operators related to the affine Lie   algebras $A^{(1)}_{r}$
  We have derived a family of equations related to the untwisted affine Lie algebras $A^{(1)}_{r}$ using a Coxeter $\mathbb{Z}_{r+1}$ reduction. They represent the third member of the hierarchy of soliton equations related to the algebra. We also give some particular examples and impose additional reductions. 
Vladimir S. Gerdjikov, Dimitar M. Mladenov, Aleksander A. Stefanov,   Stanislav K. Varbev
nlin.SI