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

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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.