Linear and Nonlinear Multichannel Scattering

Rutgers University New Brunswick, New Brunswick NJ

Investigators

Abstract

There are two main topics of research in this proposal, first, the large time behaviour and scattering theory of nonlinear Schrodinger waves off a potential term which supports many bound states. This leads to the analysis of multichannel nonlinear scattering and metastability of hamiltonian dispersive equations. The second topic involves the study of radiation damping for metastable mutltibreather solutions of the wave equation. The large time behaviour of the linearized wave equation around multibreather solutions is analyzed; a theory to estimate the lifetimes of perturbed multibreather solutions is developed and applications to nonlinear optics, in particular optical guides with non-uniform diffraction profiles. The use of optical devices and fibers in today's communication systems motivates some of the problems studied in this proposal. In particular we concentrate on the problem of effects of defects and other irregularities in optical fibers on their transport properties. We also analyze some novel optical devices made by modifying the medium in a way to achieve better filtering of noise and interchannel interference.