Summary
Two examples of the effect of nonlinearities on the scattering of nondispersive waves are presented. It is shown that nonlinear boundary conditions can lead to broadband, chaotic scattered waves when the scatterer is excited by a single wavelength plane wave. One of the examples treats a spherical scatterer in a linear elastic medium. A number of modern techniques in nonlinear analysis is used to diagnose the chaotic dynamics including Poincaré maps, fractal dimensions and Lyapunov exponents.
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Moon, F.C., Raggio, G. Chaotic scattering of waves from nonlinear scatterers. Acta Mechanica 107, 153–169 (1994). https://doi.org/10.1007/BF01201826
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DOI: https://doi.org/10.1007/BF01201826