Mathematical Sciences: Stability and Dynamics of Pulses in Nonlinear Optical Fibers

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DMS-9500615 Kath The goal this project is to analyze the effect various types of perturbations have upon the stability and dynamics of soliton solutions of the nonlinear Schroedinger equation. These perturbations include: periodic parametric forcing, stochastic noise, and higher-order linear and nonlinear derivatives. The intent is to develop and use approximate methods which allow both a simple qualitative understanding of the resulting pulse dynamics and an accurate quantitative description that is as concise as possible. The nonlinear Schroedinger equation models pulse propagation in nonlinear optical fibers, and in particular, optical solitons. As a result, an additional goal of the project is to investigate mathematically whether it is possible to use new optical fiber technologies to significantly increase the transmission speed of optical communication systems, or to improve upon the performance of these systems. One application that is being examined along these lines is the use of novel optical amplifier devices to control solitons, such as the use of phase-sensitive parametric amplifiers.