Periodically and Random Driven Dynamics in Nonlinear Optical Fibers

色散管理是将两根或多根不同色散参数的光纤串联起来，形成色散周期性变化的系统的技术。这种技术使得系统中既有高局部色散又有低平均色散成为可能。高局部色散减少了四波混频（一种在传输中扭曲信号并产生符号间干扰的效应），而低平均色散减少了长光纤跨度上色散的净累积效应。因此，总体而言，色散管理减少了对基于光纤的通信系统性能有害的影响，从而增加了传输容量。用数学术语来说，必须研究的是具有快速变化系数的非线性波动方程。这些方程的理论目前还没有得到很好的理解，将在这个奖项的支持下得到进一步的发展。本研究的主题是发展新的数学技术，用它来模拟光脉冲在非线性光纤中的传播。在光通信和信息处理系统中，正确理解这种脉冲的动力学是很重要的，这样就可以设计出新的技术来提高它们的总体容量。特别是，新的数学方法处理分散管理将被研究，以预测和提高这类系统的性能。

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.