Inverse scattering problem for the coupled-wave equations when the reflection coefficient is a rational function

To solve the inverse scattering problem in the absence of any discrete spectrum for the coupled-wave equations of the Zakharov-Shabat type when the reflection coefficient is a rational function, the coupled Gel'fand-Levitan-Marchenko integral equations are reduced to a set of linear simultaneous equations. The solution is then applied to the design of a corrugated waveguide filter.