Integrable deformations in the matrix pseudo differential operators

Inside the algebra MPsd of matrix pseudo differential operators we consider deformations of the generators of a commutative subalgebra, built out of a commutative subalgebra of the n×n-matrices of maximal dimension. The evolution equations that we impose on these generators depend of the way in which one decomposes the algebra MPsd into the direct sum of two Lie subalgebras. We treat two cases that both lead to a compatible system of Lax equations inside MPsd. These systems generalize well-known systems as the AKNS-hierarchy and the multicomponent KP hierarchy. Finally, one shows that the Lax form of the systems is equivalent to a set of zero curvature relations.