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

小行星9622802 本项目的目标是研究传播和 双折射非线性光纤中光脉冲的相互作用。 在这种光纤中，非线性、色散和双折射都发挥着重要作用，并且脉冲演变可以用数学模型来描述 两个耦合的非线性薛定谔方程。本课题 我将通过检查溶液来研究这种脉冲的传播 这些耦合方程的性质。特别是，我们将彻底 研究内部振荡，辐射和相互作用，这些 脉搏将使用分析和数值方法相结合的方法。 分析方法包括广田法和微扰法。 Hirota的方法将被用来研究相互作用的行为， 光脉冲微扰方法将被用来研究他们的 内振荡和辐射。数值方法将用于 检查分析结果，以及处理的情况下，分析 方法不合适。这项研究将提供理论 高速光纤通信设计指南 系统.此外，还将开发新的分析方法， 不可积波系 %%% 本项目将研究光的传播和相互作用 双折射非线性光纤中的脉冲。它的动机是正在进行的实验高速光纤通信系统使用孤子脉冲作为信息比特。它将解决一些基本的理论 这类电信系统设计中出现的问题。例如，它将研究脉冲信号沿光纤沿着传播的稳定性和衰减。其结果将有助于 实现基本的新通信系统， 彻底改变了整个远程信息传输领域。 ***

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. ***