Periodically and Random Driven Dynamics in Nonlinear Optical Fibers

色散管理是将具有不同色散参数的两条或多条光纤串联在一起，形成色散周期性变化的系统的技术。这种技术使得在系统中既可以具有高的局部色散又可以具有低的平均色散。高的本地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)，而低的平均色散降低了长光纤跨度上的色散的净累积效应。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不能很好地理解，并将在这个奖项的支持下得到进一步的发展。这项研究的主题是发展新的数学技术来模拟光脉冲在非线性光纤中的传播。重要的是要正确地理解光通信和信息处理系统中这种脉冲的动态，以便能够设计新的技术来增加它们的总容量。特别是，将研究处理色散管理的新的数学方法，以便预测和改善这类系统的性能。

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.