Linear and Nonlinear Multichannel Scattering

点击翻译按钮获取中文摘要

There are two main topics of research in this proposal, first, thelarge time behaviour and scattering theory of nonlinear Schrodingerwaves off a potential term which supports many bound states. This leadsto the analysis of multichannel nonlinear scattering and metastabilityof hamiltonian dispersive equations. The second topic involves the study ofradiation damping for metastable mutltibreather solutions of the waveequation. The large time behaviour of the linearized wave equation aroundmultibreather solutions is analyzed; a theory to estimate the lifetimesof perturbed multibreather solutions is developed and applicationsto nonlinear optics, in particular optical guides with non-uniform diffractionprofiles.The use of optical devices and fibers in today's communication systemsmotivates some of the problems studied in this proposal. In particularwe concentrate on the problem of effects of defects and other irregularitiesin optical fibers on their transport properties. We also analyze somenovel optical devices made by modifying the medium in a way to achievebetter filtering of noise and interchannel interference.