Mathematical Sciences: Study of Pulse Propagation in Birefringent Nonlinear Optical Fibers

9622802杨这个项目的目标是研究光脉冲在双折射非线性光纤中的传输和相互作用。在这种光纤中，非线性、色散和双折射都起着重要的作用，脉冲的演化可以用两个耦合的非线性薛定谔方程来描述。在这个项目中，我们将通过检查这些耦合方程的解的性质来研究这种脉冲的传播。特别是，我们将深入研究这些脉冲的内部振荡、辐射和相互作用。将使用解析和数值方法相结合的方法。分析方法包括Hirota方法和摄动法。Hirota的方法将用于研究光脉冲的相互作用行为。微扰方法将用来研究它们的内振荡和辐射。数值方法将被用来检查分析结果以及处理分析方法不合适的情况。本文的研究将为高速光纤通信系统的设计提供理论指导。此外，它还将为研究不可积波动系统发展新的分析方法。这个项目将研究光脉冲在双折射非线性光纤中的传输和相互作用。它的动机是正在进行的使用孤子脉冲作为信息比特的高速光纤通信系统的实验。它将解决在这种电信系统设计中出现的一些基本理论问题。例如，它将研究沿光纤传输的脉冲信号的稳定性和劣化。它的成果将有助于实现可能彻底改变整个长途信息传输领域的基础新通信系统。***

9622802 Yang The objective of this project is to study the propagation and interaction of optical pulses in birefringent nonlinear optical fibers. In such fibers, nonlinearity, dispersion and birefringence all play an important role, and the pulse evolution can be modelled mathematically by two coupled nonlinear Schroedinger equations. In this project, we will study the propagation of such pulses by examining the solution properties of these coupled equations. In particular, we will thoroughly investigate the internal oscillations, radiation and interaction of these pulses. A combination of analytical and numerical methods will be used. The analytical methods include Hirota's method and the perturbation methods. Hirota's method will be used to study the interaction behaviors of the optical pulses. The perturbation methods will be used to study their internal oscillations and radiation. The numerical methods will be used to check the analytical results as well as to deal with cases where analytical methods are not appropriate. The proposed research will provide theoretical guidance to the design of the fast-speed fiber-optic telecommunication systems. In addition, it will develop new analytical methods for studying non-integrable wave systems. %%% This project will study the propagation and interaction of optical pulses in birefringent nonlinear optical fibers. It is motivated by the ongoing experiments on high-speed fiber-optic telecommunication systems using solitonian pulses as information bits. It will address some basic theoretical questions arising in the design of such telecommunication systems. For instance, it will study the stability and degradation of pulse signals travelling along the optical fibers. Its results will contribute to the realization of the underlying new communication systems which could revolutionize the whole field of long-distance information transmission. ***