An efficient algorithm for solving Zakharov-Shabat inverse scattering problem

An efficient numerical method for solving Zakharov-Shabat (ZS) inverse scattering problem is presented. In this method, instead of equivalent second-order differential equations to the Gel'fand-Levitan-Marchenko (GLM)-type integral equations, equivalent first-order differential equations are adopted and sufficiently accurate solutions to Zakharov-Shabat inverse problem can be achieved without iterations. Examples for applying it to design nonuniform transmission line (NTL) filters are also provided.