Eigen Value Problem with Nonvanishing Potentials

抄録

The eigen value problem of Zakharov-Shabat type with nonvanishing potentials q(x) and r(x) where q(−∞)r(−∞)=q(+∞)r(+∞)≠0 can be transformed to such an adequate form by which the inverse problem can be described systematically. The analytical properties of Jost functions and scattering data are made clear under certain integrable conditions of potentials. As an example, the inverse problem about the case of wave modulation in a stable medium has been solved.