Nonvanishing boundary condition for the mKdV hierarchy and the Gardner   equation
  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. 
J. F. Gomes, Guilherme S. Fran\c{c}a, A. H. Zimerman
nlin.SI math-ph math.MP