Noncommutative Generalized NS and Super Matrix KdV Systems from a   Noncommutative Version of (Anti-) Self-Dual Yang-Mills Equations
  A noncommutative version of the (anti-) self-dual Yang-Mills equations is shown to be related via dimensional reductions to noncommutative formulations of the generalized (SO(3)/SO(2)) nonlinear Schrodinger (NS) equations, of the super-Korteweg- de Vries (super-KdV) as well as of the matrix KdV equations. Noncommutative extensions of their linear systems and bicomplexes associated to conserved quantities are discussed. 
M. Legare