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.

该提案中有两个主要主题，首先是非线性schrodingerwavave的thelarge时间行为和散射理论，这些术语支持许多有限状态。这领导了对哈密顿分散方程的多通道非线性散射和亚稳定性的分析。第二个主题涉及对波动的亚稳态mutltibreather溶液进行放射阻尼的研究。分析了跨核溶液周围线性波动方程的较大时间行为。开发了一种估计摄取多凝胶溶液的寿命的理论，并开发了非线性光学器件，特别是具有非均匀衍射式Profiles的光学指南。在当今的通信系统中，使用光学设备和纤维在此提案中研究了一些问题。特别是，我们专注于缺陷和其他不规则性纤维对运输特性的影响的问题。我们还通过以实现噪声和通道间干扰的方式修改介质来分析了Somenovel光学设备。