Chaotic Dynamics in Near-Integrable Systems and the Role of Symmetries

该奖项将支持非线性光学介质数学模型的研究。这些模型具有可积的非线性偏微分方程的形式，即在某种意义上可以完全线性化，以及这些方程的摄动。本研究的目标是进一步了解这些模型的混沌激励机制，并获得对应于周期或单脉冲波形的特定解。理论结果也将用作数值计算方案的基准问题。光纤和环形激光腔等光介质的数学模型具有非线性微分方程的形式。本研究将探讨预测此类介质行为的此类模型的特性。例子包括沿着这种光纤传播的光脉冲的自然形状和持续时间，以及介质中自发产生的噪声。

This award will support research on mathematical models for nonlinear optical media. These models have the form of nonlinear partial differential equations that are integrable, i.e. that can be completely linearized in a certain sense, and of perturbations of such equations. The goal of the research is to further our understanding of chaotic excitation mechanisms for such models and to obtain specific solutions that correspond to periodic or single-pulsewaveforms. The theoretical results will also be used as benchmark problems fornumerical computation schemes.Mathematical models for optical media such as optical fibers and ring-lasercavities have the form of nonlinear differential equations. This research will address properties of such models that predict the behavior of such media.Examples include the natural shape and duration of light pulses that can travel along such fibers and the spontaneous generation of noise within the medium.