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

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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.