Linear and Nonlinear Multichannel Scattering

线性和非线性多通道散射

• 批准号: 0100490
• 负责人: Avraham Soffer
• 金额: $ 12.6万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-06-01 至 2005-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0100490&HistoricalAwards=false
• 关键词: Linear; Nonlinear; Multichannel; Scattering

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.

本文主要研究两个问题：一是支持多束缚态的势项下非线性薛定谔波的大时行为和散射理论。这导致了对哈密顿色散方程的多通道非线性散射和亚稳态的分析。第二个主题涉及波方程亚稳态多呼吸解的辐射阻尼研究。分析了多呼吸解下线性化波动方程的大时态；本文提出了一种估计摄动多呼吸解寿命的理论，并将其应用于非线性光学，特别是具有非均匀衍射轮廓的光学波导。光学设备和光纤在当今通信系统中的使用激发了本提案中研究的一些问题。我们特别关注光纤中缺陷和其他不规则性对其输运特性的影响问题。我们还分析了一些通过改变介质来实现更好地滤除噪声和信道间干扰的新型光学器件。