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Nonlinear waves: Dynamics and transport. (English) Zbl 0735.76007
Summary: Interfacial waves illustrate a wide variety of nonliner effects including: multiple stationary states; bifurcations affected by symmetry; low-dimensional chaotic dynamics; patterns with long range order; and secondary instabilities leading to spatiotemporal chaos. Theoretical descriptions based on amplitude equations have been quite successful in describing many of these phenomena. Recent experiments on the transport and mixing properties of capillary waves show that particle trajectories can follow Brownian statistics, while concentration fields acquire fractal structure.

MSC:
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76B45 Capillarity (surface tension) for incompressible inviscid fluids
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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