Analytical and numerical solution to the two-potential Zakharov-Shabat inverse scattering problem

An analytical and a numerical method are presented in order to solve the inverse scattering problem associated with the two-potential Zakharov-Shabat coupled mode equations. The numerical solution, which uses leapfrogging in space and time, represents a direct numerical solution to the coupled Gel´fand-Levitan-Marchenko (GLM) integral equations as an extension of the authors´ previous work on GLM equations of simpler form. The analytical method, which is applied for one-pole reflection coefficients, consists in constructing appropriate differential operators which transform the coupled GLM equations to ordinary linear differential equations. An application of these methods for nonuniform transmission line synthesis is presented