Mathematical Sciences: Dynamics of Pulses in Nonlinear Optical Waveguides

在这一奖项的支持下，主要研究者将把他关于非线性薛定谔系统单孤子解的无穷线Kaup-Newell微扰理论的一些工作推广到多孤子情况。这项工作适用于波包形式的数据在非线性光纤中的传输，因此它与利用光纤技术的现代通信系统的设计高度相关。主要研究人员将使用基于渐近性的方法来研究非线性偏微分方程组的解的行为。似乎每天，报纸上都有关于光纤技术在现代通信系统设计中的使用的文章。事实上，电话公司和计算机公司对设计“无损”传输数据的方式非常感兴趣。一种可能的解决方案是基于光纤的新兴技术，因为光纤提供了在没有显著色散或失真的情况下传输数据的潜力。凭借这一奖项，首席研究员将研究描述波在光纤中传播的非线性方程组的解。

In the work supported by this award the principal investigator will extend some of his work on the infinite-line Kaup-Newell perturbation theory for a single soliton solution of a nonlinear Schroedinger system to the multiple soliton case. This work has applications to the transmission of data in the form of wave packets through nonlinear optical fibers, and so such it is highly relevant to the design of modern communications' systems that utilize optical fiber technology. The principal investigator will employ methods based upon asymptotics in order to study the behavior of solutions of nonlinear systems of partial differential equations. Every day, it seems, there are articles in the newspapers about the use of fiber optics technologies in the design of modern communications systems. Indeed, telephone companies and computer companies are very much interested in designing "lossless" ways of transmitting data. One possible solution is the emerging technologies based upon fiber optics, since fiber optics affords the potential of transmitting data without significant dispersion or distortion. With this award the principal investigator will study solutions of the nonlinear system of equations that describes the propagation of waves through optical fibers.