Dressing Technique for Intermediate Hierarchies

TL;DR

This paper extends the dressing technique to generalized AKNS systems, enabling the construction of solutions using matrix pseudo-differential operators and formal series, thus advancing the integrability framework for these hierarchies.

Contribution

It introduces a generalized dressing method applicable to a broader class of AKNS hierarchies, enhancing solution-generating techniques.

Findings

Dressing technique developed for generalized AKNS systems.

Application of matrix pseudo-differential operators in the dressing process.

Formal series approach with respect to the spectral parameter.

Abstract

A generalized AKNS systems introduced and discussed recently in \cite{dGHM} are considered. It was shown that the dressing technique both in matrix pseudo-differential operators and formal series with respect to the spectral parameter can be developed for these hierarchies.