Integrable mappings for noncommuting objects
  We construct hierarchies of integrable systems invariant under the two-dimensional Darboux-Toda mapping for noncommuting objects, thus generalizing to the noncommutative case the integrable mapping approach to nonlinear dynamical systems. Besides the usual setup with one time and two space dimensions, we consider the case when the unknown functions also depend on two Grassman variables. 
Andrei N. Leznov and Emil A. Yuzbashyan