Dispersive Shocks in Continuous & Discrete Media

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9500623 Venakides The proposal focuses on the study of dispersive wave generation and propaeation through nonlinear discrete or continuous media. The phenomena involve the interaction between two different space-time scales. The small scale consists of strongly nonlinear single or multiple traveling waves with wave parameters that vary in the large scale. The waves, that eventually spread over large space regions are generated at points where the dispersive nature of the system smoothens the shocks produced by the nonlinearity. An oscillatory microstructure will thus typically arise out of non-oscillatory initial data. The proposed projects are relevant to physical applications that involve nonlinearity and dispersion. Such applications, include electron flow in quantum semiconductor devices and the effect of impurities in the transmission characteristics in solid state devices. Our study of nonlinear particle chains is to a great extent motivated by the desire to understand basic properties of materials through their microscopic structure.