  The Drinfeld-Sokolov reduction method has been used to associate with $gl_n$
extensions of the matrix r-KdV system. Reductions of these systems to the fixed
point sets of involutive Poisson maps, implementing reduction of $gl_n$ to
classical Lie algebras of type $B, C, D$, are here presented. Modifications
corresponding, in the first place to factorisation of the Lax operator, and
then to Wakimoto realisations of the current algebra components of the
factorisation, are also described.
