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Bäcklund transformations for high-order constrained flows of the AKNS hierarchy: canonicity and spectrality property

Yunbo Zeng·Huihui Dai·Jinping Song
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Abstract

New infinite number of one- and two-point Bäcklund transformations (BTs) with explicit expressions are constructed for the high-order constrained flows of the AKNS hierarchy. It is shown that these BTs are canonical transformations including Bäcklund parameter $η$ and a spectrality property holds with respect to $η$ and the 'conjugated' variable $μ$ for which the point $(η, μ)$ belongs to the spectral curve. Also the formulas of m-times repeated Darboux transformations for the high-order constrained flows of the AKNS hierarchy are presented.

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Yunbo Zeng, Huihui Dai, Jinping Song. 2001-12-11. Bäcklund transformations for high-order constrained flows of the AKNS hierarchy: canonicity and spectrality property. https://doi.org/10.1088/0305-4470%2F35%2F4%2F320

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