Mathematical Sciences: Mathematical Studies of Wave Propagation

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9510492 Hile This work is supported by a Research Planning Grant for Women Scientists and Engineers Award. The goal of the research is two-fold: (i) to understand which higher-order dispersive and nonlinear effects cause the asymmetry apparent in certain one-dimensional solutions of Maxwell's equations describing ultra-short optical soliton-like pulses, and to determine if a corresponding extended nonlinear Schroedinger equation can be developed to describe the asymmetric pulses produced in pulse- compression experiments; and (ii) to determine the physical parameters responsible for the divergence or collapse of two-dimensional ultra-short spatial solitons propagating in a planar waveguide. The project will also involve planning activities in collaboration with a senior mathematician from industry to determine the feasibility of developing an innovative technique for efficiently predicting high-frequency radar cross-section statistics for realistic, complex targets. Over the last decade, optical fiber communication systems have played a vital role in revolutionizing the telecommunications industry. Though this technology has progressed very rapidly, advances continue to be made in the design of these systems. Areas of current research in the field, which hold great interest and challenge for mathematicians, involve physical phenomena and processes that exploit the nonlinear effects in optical materials. These physical phenomena and processes include optical solitons, optical pulse compression, and optical switching. This project will involve goals and planning activities that include developing and analyzing mathematical models of these nonlinear phenomena and processes in order to improve the design of optical communications systems. The National Science Foundation's mandate to ensure the vitality of the Nation's scientific enterprise includes concern for the quality, composition, distribution and effectiveness of the human resou rce base in science and engineering. Within this context, the Foundation is committed to enhancing the current rate of participation of women in science and engineering careers, in general, and as active participants in all of its programs. Research Planning Grant awards are made: (1) to help increase the number of new women investigators participating in NSF's research programs; and, (2) to facilitate preliminary studies and other activities related to the development of competitive research projects and proposals by women who have not previously had independent Federal research funding. Research Planning Grants are one-time awards that may be used for preliminary work to determine the feasibility of a proposed line of inquiry, and/or for other activities that will facilitate proposal development.