Inverse scattering for scattering data with poor regularity of slow decay (Q1822742)

The author studies the inverse scattering problem for scattering data with poor regularity and slow decay properties via a standard method of Fadeev. Immediate applications may be given of the results to the Cauchy problem for the Korteweg-de Vries equations with irregular initial profile such as a steplike smoothed Heavyside function. An extremely detailed and systematic study is made in the paper of the Marchenko equation in \(L_ 2({\mathbb{R}}_-)\) which in fact offers a succinct and excellent introduction to this theory.