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.
Categories: hep-th nlin.SI