Time-evolution-proof Scattering Data for the Focusing and Defocusing Zakharov-Shabat Systems
Time-evolution-proof Scattering Data for the Focusing and Defocusing Zakharov-Shabat Systems
In this article we give sufficient conditions on the scattering data of a defocusing or focusing Zakharov-Shabat system in order that its potential is square integrable. For a dense subset of integrable as well as square integrable potentials, we show that the scattering data actually satisfy these sufficient conditions.