Canonical explicit Bäcklund transformations with spectrality for constrained flows of soliton hierarchies

Abstract

It is shown that explicit Bäcklund transformations (BTs) for the high-order constrained flows of soliton hierarchy can be constructed via their Darboux transformations and Lax representation, and these BTs are canonical transformations including Bäcklund parameter $\eta$ and possess a spectrality property with respect to $\eta$ and the 'conjugated' variable $\mu$ for which the pair $(\eta ,\mu )$ lies on the spectral curve. As model we present the canonical explicit BTs with the spectrality for high-order constrained flows of the Kaup-Newell hierarchy and the KdV hierarchy.

21 pages, Latex, to be published in "PHYSICA A"

References in corpus (3)

• Backlund transformations for many-body systems related to KdV
• Backlund transformations for the sl(2) Gaudin magnet
• Bäcklund transformations for high-order constrained flows of the AKNS hierarchy: canonicity and spectrality property