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

这个项目的目标是分析不同类型的扰动对非线性薛定谔方程孤子解的稳定性和动力学的影响。这些扰动包括：周期性参数强迫、随机噪声、高阶线性和非线性导数。其目的是开发和使用近似方法，既可以对所产生的脉冲动力学进行简单的定性理解，又可以尽可能简明地进行准确的定量描述。非线性薛定谔方程模拟了脉冲在非线性光纤中的传播，特别是光孤子。因此，该项目的另一个目标是从数学上研究是否有可能使用新的光纤技术来显着提高光通信系统的传输速度，或者改善这些系统的性能。沿着这条路线正在研究的一个应用是使用新型光放大器器件来控制孤子，例如使用相敏参数放大器。

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.