Fine structure of the discrete transformation for multicomponent   integrable systems
  It is shown that in the case of multicomponent integrable systems connected with algebras $A_n$, the discrete transformation $T$ possesses the fine structure and can be represented in the form $T=\prod T_i^{l_i}$, where $T_i$ are n commuting basis discrete transformations, and $l_i$ are arbitrary natural numbers. All the calculations are conducted in detail for the case of a 3-wave interacting system. 
A.N. Leznov, J. Escobedo-Alatorre, and R.Torres-Cordoba