  In this paper we provide an algebraic construction for the negative even mKdV
hierarchy which gives rise to time evolutions associated to even graded Lie
algebraic structure. We propose a modification of the dressing method, in order
to incorporate a non-trivial vacuum configuration and construct a deformed
vertex operator for $\hat{sl}(2)$, that enable us to obtain explicit and
systematic solutions for the whole negative even grade equations.
