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

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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.