The hard pulse approximation for the AKNS 2 × 2-system

In the hard pulse approximation, commonly used in nuclear magnetic resonance, one considers potentials for the AKNS system that are sums of δ-functions. The system of differential equations does not, strictly speaking make sense for such potentials. In [8] an analogous discrete forward and inverse problem are analyzed. We review these results and show that pulses obtained using the inverse scattering transform for this hard pulse approximation converge to the expected continuum potential pointwise and in the L1-norm. We also show that the AKNS system makes sense with potentials that are nonatomic measures with finite total variation.