Mathematical Sciences: Surface Wave Mode Interactions with Explicit and Hidden Symmetry

首席研究员将研究当前在圆形和方形几何中进行的参数驱动表面波实验中提出的各种问题。物理系统的几个模型似乎在其自然几何对称的背景下表现出非一般的分岔，因为分岔的有效对称性大于自然对称性。这些研究将试图解释这些明显隐藏的对称性。非线性水动力波的分析是重要的，因为它们在自然界中广泛存在，因为这种分析可以作为其他情况的原型。

The principal investigator will study a variety of problems raised by current experiments on parametrically driven surface waves performed in circular and square geometries. Several models for physical systems appear to exhibit bifurcations that are non-generic in the context of their natural geometric symmetry in that the effective symmetry of the bifurcation is larger than the natural symmetry. These studies will attempt to explain these apparent hidden symmetries. The analysis of nonlinear hydrodynamic waves is important because of their wide spread occurrence in nature and because such analyses can serve as a prototype for other situations.