Mathematics Colloquia and Seminars

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The propagation of nonlinear waves in uniform media is typically described by nonlinear, translation invariant, Hamiltonian partial differential (or integro-differential) equations. Nonlinearity leads to interactions between the Fourier components of the wave, and various phenomena, such as the formation of singularities, may be analyzed from a spatial or a spectral (Fourier) perspective. We will illustrate these ideas using the inviscid Burger's equation as an example. After that, we will discuss a related integro-differential equation that describes the propagation of nonlinear hyperbolic surface waves, such as the Rayleigh surface waves that are generated by earthquakes.