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

Yunbo Zeng·Yiqing Zhu·Ting Xiao·Huihui Dai
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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 $η$ and possess a spectrality property with respect to $η$ and the 'conjugated' variable $μ$ for which the pair $(η, μ)$ 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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Yunbo Zeng, Yiqing Zhu, Ting Xiao, Huihui Dai. 2001-11-21. Canonical explicit Bäcklund transformations with spectrality for constrained flows of soliton hierarchies. https://doi.org/10.1016/s0378-4371(01)00550-7

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