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 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).
