Negative Even Grade mKdV Hierarchy and its Soliton Solutions

Abstract

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 $\widehat{sl}(2)$, that enable us to obtain explicit and systematic solutions for the whole negative even grade equations.

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• SKdV, SmKdV flows and their supersymmetric gauge-Miura transformations
• Twisted Affine Integrable Hierarchies and Soliton Solutions
• New negative grade solitonic sector for supersymmetric KdV and mKdV hierarchies
• New soliton solutions for Chen-Lee-Liu and Burgers hierarchies and its Bäcklund transformations