ONE-DIMENSIONAL INVERSE SCATTERING: EXACT METHODS AND APPLICATIONS
Abstract
In this report new methods are developed to solve coupled integral equations of the Gel'fand-Levitan-Marchenko type. First, an iterative numerical method which uses leapfrogging in time and space is developed to solve the inverse scattering problem associated with the Zakharov-Shabat coupled mode equations. Second, both an analytical and a numerical method are developed for solving the corresponding two-potential inverse scattering problem and they are applied in order to synthesize lossy nonuniform transmission lines. The analytical method is based on the construction of appropriate differential operators transforming the integral equations to linear differential equations which can be easily solved, while the numerical method consists in a generalization of the iterative numerical method mentioned above. Furthermore, a numerical technique of successive kernel approximations is developed in order to solve coupled Gel'fand-Levitan-Marchenko integral equations which appear in a formulation of the inverse scattering problem associated with energy-dependent Schrodinger potentials and lossy inhomogeneous dielectrics. Subsequently, a numerical implementation of these problems is performed. The solutions resulting from the methods developed here are compared with those based on independent methods of they are reduced to known results in some special cases. Finally, possible applications of this work in other areas such as integrated optics and soliton theory are indicated. ^
Subject Area
Engineering, Electronics and Electrical
Recommended Citation
PANAYIOTIS VASSILIOS FRANGOS,
"ONE-DIMENSIONAL INVERSE SCATTERING: EXACT METHODS AND APPLICATIONS"
(January 1, 1986).
Dissertations available from ProQuest.
Paper AAI8623989.
http://repository.upenn.edu/dissertations/AAI8623989