Darboux Transformations from Reductions of the KP Hierarchy

TL;DR

This paper discusses the construction of Darboux transformations for Lax pairs, including binary transformations that preserve properties like self-adjointness, with applications to reductions of the KP hierarchy such as BKP and CKP.

Contribution

It introduces a general method for constructing Darboux transformations that maintain specific properties and applies it to multicomponent BKP and CKP reductions of the KP hierarchy.

Findings

Developed a framework for binary Darboux transformations preserving operator properties.

Applied the framework to multicomponent BKP and CKP reductions.

Enhanced understanding of transformations within the KP hierarchy.

Abstract

The use of effective Darboux transformations for general classes Lax pairs is discussed. The general construction of ``binary'' Darboux transformations preserving certain properties of the operator, such as self-adjointness, is given. The classes of Darboux transformations found include the multicomponent BKP and CKP reductions of the KP hierarchy.