Nonvanishing boundary condition for the mKdV hierarchy and the Gardner equation

Abstract

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