Inverse Scattering Theory

Duke University, Durham NC

Investigators

Abstract

DMS-0071398 The project contains five research problems: 1. Analytic properties for scattering/inverse scattering transforms. 2. Perturbation on NLS. 3. Perturbation for Toda lattice. 4. Random matrices. 5. Multiple orthogonal polynomials. All these problems will be studied via the Riemann--Hilbert problem approach, which has shown tremendous potential in solving various integrable problems in broad sense. This project analyzes several mathematical problems ranging from partial differential equations, random matrices, to the approximation theory. Some of these problems have pure mathematical interest and others have applications in physics and engineering. One of such applications is the soliton solutions of the perturbed nonlinear Schrodinger equation. These soliton solutions are used in the fiber optical transmission.