Periodically and Random Driven Dynamics in Nonlinear Optical Fibers

色散管理是将两条或多条具有不同色散参数的光纤连接起来形成色散周期性变化的系统的技术。 该技术使得系统中可以同时具有高局部色散和低平均色散。 高局部色散减少了四波混频（一种使信号失真并在传输中产生码间干扰的效应），而低平均色散则减少了长光纤跨度上色散的净累积效应。 因此，总的来说，色散管理减少了对基于光纤的通信系统的性能不利的影响，从而允许增加传输容量。 用数学术语来说，必须研究的是系数快速变化的非线性波动方程。这些方程的理论目前还没有被很好地理解，并将在该奖项的支持下得到推进。这项研究的主题是开发新的数学技术来模拟非线性光纤中光脉冲的传播。 正确理解光通信和信息处理系统中此类脉冲的动态非常重要，以便设计新技术来提高其整体容量。 特别是，将研究处理色散管理的新数学方法，以预测和提高此类系统的性能。

Dispersion management is the technique of concatenating two or more optical fibers with different dispersion parameters to form a system with periodically varying dispersion. This technique makes it is possible to have both high local and low average dispersion in the system. The high local dispersion reduces four-wave mixing (an effect that distorts signals and produces intersymbol interference in transmissions), while the low average dispersion reduces the net cumulative effects of dispersion over long optical fiber spans. Overall, therefore, dispersion management reduces effects which are detrimental to the performance of optical-fiber based communication systems, thus allowing transmission capacity to be increased. In mathematical terms, what must be studied are nonlinear wave equations with rapidly varying coefficients. The theory of these equations is currently not well understood and will be advanced with support from this award. The theme of this research is the development of new mathematical techniques with which to model the propagation of optical pulses in nonlinear optical fibers. It is important to properly understand the dynamics of such pulses in optical communication and information processing systems so that new techniques can be devised to increase their overall capacity. In particular, new mathematical methods for dealing with dispersion managementwill be investigated, in order to predict and improve the performance of such systems.