Unique reconstruction of the inverse spectral problem with mixed data for AKNS operator

Abstract In this paper, the inverse spectral problem of the AKNS operator ℋ ⁢ ( p , q ) {\mathcal{H}(p,q)} defined on the interval [ 0 , 1 ] {[0,1]} with the potential pair ( p , q ) {(p,q)} being a priori known on the subinterval [ 0 , r m ] {[0,\frac{r}{m}]} with 0 < r m < 1 2 {0<\frac{r}{m}<\frac{1}{2}} is considered. An algorithm of reconstruction of the potential from the knowledge of a full spectrum together with a subset of the norming constants is established.