Inverse scattering: solution of coupled Gel´fand-Levitan-Marchenko integral equations using successive kernel approximations

We develop a method of successive kernel approximations to solve coupled Gel´fand-Levitan-Marchenko (1955) integral equations. These equations appear in the synthesis problem of nonuniform and lossy transmission lines, the inversion of absorbing dielectrics and wavenumber-dependent potentials, the design of corrugated waveguide filters, soliton theory, and other applications. We find that our method is easy to apply, more accurate than previously developed methods, and can be used for a larger number of applications when compared to prior work. As an application and example, wavenumber-dependent potentials are reconstructed from scattering data