On the Dressing Method for the Generalised Zakharov--Shabat System

TL;DR

This paper extends the dressing method for the Generalised Zakharov--Shabat system to orthogonal and symplectic Lie algebras, explicitly constructing dressing factors and deriving soliton solutions for related nonlinear equations.

Contribution

It introduces explicit dressing factors for systems associated with orthogonal and symplectic Lie algebras, expanding the applicability of the dressing method.

Findings

Constructed explicit dressing factors for new Lie algebra classes.

Derived soliton solutions for specific nonlinear evolution equations.

Extended the dressing method beyond sl(N) systems.

Abstract

The dressing procedure for the Generalised Zakharov--Shabat system is well known for systems, related to sl(N) algebras. We extend the method, constructing explicitly the dressing factors for some systems, related to orthogonal and symplectic Lie algebras. We consider 'dressed' fundamental analytical solutions with simple poles at the prescribed eigenvalue points and obtain the corresponding Lax potentials, representing the soliton solutions for some important nonlinear evolution equations.