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

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

2001-11-21

arxiv.org/abs/nlin/0111046v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

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

Scientific paper

10.1016/S0378-4371(01)00550-7

It is shown that explicit B\"{a}cklund 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 B\"{a}cklund 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.

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