  We construct the hierarchy of a multi-component generalisation of modified
KdV equation and find exact solutions to its associated members. The
construction of the hierarchy and its conservation laws is based on the
Drinfel'd-Sokolov scheme, however, in our case the Lax operator contains a
constant non-regular element of the underlying Lie algebra. We also derive the
associated recursion operator of the hierarchy using the symmetry structure of
the Lax operators. Finally, using the rational dressing method, we obtain the
one soliton solution, and we find the one breather solution of general rank in
terms of determinants.
