Interdisciplinary Research and Education in Nonlinear Optics, Mathematics and Electrical Engineering

这是数学科学项目跨学科资助下的一项具有教育重点的研究提案。这位首席研究员将在1998-99学年(和1998年夏天)在弗吉尼亚理工大学电气工程系学习通信网络理论的基础知识，并建立用于通信的非线性光纤研究计划。PI专门计划研究非线性薛定谔方程的光谱方法，该方程对通信光纤中的脉冲传播进行建模。他建议通过数值方法和扩展的多尺度方法来考虑方程，这两种方法都是在谱域而不是在时间域。由此得到的渐近分析和伴随的数值分量对于通信工程师在非线性效应显著的情况下模拟脉冲在光纤中的传输将是非常有价值的。由此产生的分析也将引起数学研究人员和教师的浓厚兴趣。因此，国际数学联合会希望参与创造新的数学思想，以满足新兴技术的需要。这位研究人员计划通过研讨会、座谈会、会议和出版物与他的数学同事分享他的发现。他建议通过硕士论文水平的工作和本科生的研究项目让学生参与到他的研究中来。除了教职员工和研究生，PI还计划通过他所在系的本科生研究计划，让数学专业的本科生更容易接触到光纤通信的数学方面。这是一个自1995年春季学期以来一直存在的本科生数学研究的活跃项目。(见http://www.math.vt.edu/UR_brochure/URbrochure.html)网站)这一国际综合管理系统项目由重大计划多学科活动办公室和数学科学司共同支持。

This is a research proposal with an educational emphasis under the Interdisciplinary Grants in the Mathematical Sciences program. The principle investigator will spend the 1998-99 academic year (and summer, 1998) in the Electrical Engineering department at Virginia Tech University learning the fundamentals of communications network theory and building a research program in nonlinear fiber optics for communications. The PI plans specifically to study spectral approaches to the nonlinear Schrodinger equation, which models pulse propagation in communications fibers. He proposes consideration of the equation both numerically and through extended multiple scales methods, both of which are in the spectral domain rather than the time domain. The resulting asymptotic analysis, with accompanying numerical component, would be extremely valuable to communications engineers in their efforts to simulate pulse transmission in fibers where nonlinear effects are significant. The resulting analysis would also be of keen interest to researchers and teachers of mathematics. The PI therefore expects to be involved in the creation of new mathematical ideas to meet the needs of emerging technology. The investigator plans to share his findings with his mathematical colleagues through seminars, colloquia, conferences and publications. He proposes to involve students in his findings through masters thesis level work and through undergraduate research projects. In addition to faculty colleagues and graduate students, the PI also plans to make the mathematical aspects of fiber communications more accessible to undergraduate mathematics major through his department's Undergraduate Research Program. This is an active program in undergraduate research in mathematics which has been in existence since the spring semester of 1995. (see the web site at http://www.math.vt.edu/UR_brochure/URbrochure.html) This IGMS project is jointly supported by the MPS Office of Multidisciplinary A ctivities (OMA) and the Division of Mathematical Sciences (DMS).