Stochastically driven dynamical systems

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Abstract
Initially, this study arose from questions concerning the scattering of tsunamis as they propagate over the irregular topography of the deep waters of the ocean. The mathematical problem to which this led is pertinent to many other phenomena, however, and we direct the analysis, here, to the propagation of gravity waves over an irregular bottom topography and to the lateral oscillations of an elastic string whose ends undergo random longitudinal displacements. Several facets of the mathematical problem are rather fascinating but the results do suggest that scattering is not the most important part of the tsunami propagation.

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