A Kac-Moody algebra construction for the integrable hierarchy containing the
Gardner equation is proposed. Solutions are systematically constructed
employing the dressing method and deformed vertex operators which takes into
account the nonvanishing boundary value problem for the mKdV hierarchy.
Explicit examples are given and besides usual KdV like solitons, our solutions
contemplate the large amplitude table-top solitons, kinks, dark solitons,
breathers and wobbles
