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 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.

References in corpus (2)

• Wobbles and other kink-breather solutions of the Sine Gordon model
• Algebraic properties of Gardner's deformations for integrable systems

Cited by in corpus (5)

• The algebraic structure behind the derivative nonlinear Schroedinger equation
• On the mKdV-Liouville hierarchy and its self-similarity reduction
• SKdV, SmKdV flows and their supersymmetric gauge-Miura transformations
• New soliton solutions for Chen-Lee-Liu and Burgers hierarchies and its Bäcklund transformations
• New negative grade solitonic sector for supersymmetric KdV and mKdV hierarchies