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

这是一个研究建议与教育重点下的跨学科赠款在数学科学计划。主要研究员将在弗吉尼亚理工大学电气工程系度过1998-99学年（和1998年夏天），学习通信网络理论的基础知识，并建立通信非线性光纤的研究项目。 PI计划专门研究非线性薛定谔方程的光谱方法，该方程模拟了通信光纤中的脉冲传播。他建议考虑方程的数值和通过扩展的多尺度方法，这两种方法都是在谱域，而不是时域。由此产生的渐近分析，伴随着数值分量，将是非常有价值的通信工程师在他们的努力，以模拟光纤中的脉冲传输的非线性效应是显着的。 由此产生的分析也会引起数学研究人员和教师的浓厚兴趣。 因此，PI希望参与创造新的数学思想，以满足新兴技术的需求。 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研究项目让学生参与他的研究结果。 除了教师同事和研究生，PI还计划通过他的部门的本科研究计划，使光纤通信的数学方面更容易为本科数学专业。 这是一个积极的计划，在本科生的研究数学，自1995年春季学期已经存在。 (see网址为 http://www.math.vt.edu/UR_brochure/URbrochure.html) 该IGMS项目由MPS多学科活动办公室（OMA）和数学科学部（DMS）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).