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

A new infinite number of one- and two-point Backlund 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 the Backlund 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. In addition, the formulae of m-times repeated Darboux transformations for the high-order constrained flows of the AKNS hierarchy are presented.