Mathematical Sciences: Waves and Instabilitites in Optical Fibers and Nonlinear Media

数学科学：光纤和非线性介质中的波和不稳定性

• 批准号: 9508634
• 负责人: Philip Holmes
• 金额: $ 7.1万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-10-01 至 1997-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9508634&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Waves; Instabilitites; Optical

9508634 Holmes The University-Industry Cooperative Research Programs in the Mathematical Sciences are programs designed to establish a mechanism for exchange of mathematical scientists between academia and industry at different stages of their careers. These programs will strengthen the links between industry and academia and identify and encourage new avenues of research in the mathematical sciences. The University-Industry Postdoctoral Research Fellowships provide two years of support for recent recipients of doctoral degrees in the mathematical sciences. These awards are a means of contributing to the future vitality of the scientific effort of the nation. The postdoctoral fellow will work closely with scientific advisors from both academia and industry. Jose Nathan Kutz received his doctoral degree from Northwestern University and will work under the direction of Philip Holmes at Princeton and Paul Wright and Pierre Hohenberg at AT&T. The research will deal with optical fiber technology and nonlinear wave propagation and pattern formation in spatially extended systems. The common mathematical ground linking these areas is the use of nonlinear partial differential equations in modeling wave and pulse propagation in active and disordered media. In particular, equations of nonlinear Schroedinger (NLS) and Ginsburg-Landau type frequently arise.

9508634霍姆斯数学科学中的大学与产业合作研究项目是旨在为学术界和产业界在其职业生涯的不同阶段交流数学科学家的机制而设计的项目。这些计划将加强产业界和学术界之间的联系，并确定和鼓励数学科学研究的新途径。大学-工业博士后研究奖学金为最近获得数学科学博士学位的人提供两年的支持。这些奖项是为国家科学努力的未来活力做出贡献的一种手段。这位博士后研究员将与学术界和工业界的科学顾问密切合作。何塞·内森·库茨在西北大学获得博士学位，他将在普林斯顿大学的菲利普·霍姆斯以及美国电话电报公司的保罗·赖特和皮埃尔·霍亨伯格的指导下工作。这项研究将涉及光纤技术以及空间扩展系统中的非线性波传播和图案形成。连接这些领域的共同数学基础是使用非线性偏微分方程来模拟波和脉冲在活动和无序介质中的传播。特别是，非线性薛定谔(NLS)方程和Ginsburg-Landau型方程经常出现。