Characterization of Scattering Data for the AKNS System
We characterize the scattering data of the AKNS system with vanishing boundary conditions. We prove a 1,1-correspondence between L 1-potentials without spectral singularities and Marchenko integral kernels which are sums of an L 1 function (having a reflection coefficient as its Fourier transform) and a finite exponential sum encoding bound states and norming constants. We give characterization results in the focusing and defocusing cases separately.
scattering data akns system characterization problem zakharov-shabat system inverse scattering transform