Singularities And Classifications Of Integrable Systems

哪些工程和自然的数学模型排除了混沌，并且具有全球可预测的解决方案？在像光子学和量子引力这样的不同领域中，普遍存在哪些模型？答案就在可积系统理论中。我们的目标是开发强大的新算法来识别可积模型并推导出它们的显着性质。预计这些算法将回答当代重要的基本问题。从长远来看，可能的成果包括在非线性光学和量子计算方面的应用。

What mathematical models of engineering and nature exclude chaos and have globally predictable solutions? What models occur ubquitously in fields as diverse as photonics and quantum gravity? The answers lie in the theory of integrable systems. We aim to develop powerful new algorithms for identifying integrable models and for deducing their remarkable properties. These algorithms are expected to answer fundamental questions of contemporary importance. Longer term possible outcomes include applications to nonlinear optics and quantum computing.