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Solitary wave decay in non-linear Faraday resonance. (English) Zbl 0935.76030
Summary: We investigate possible mechanisms by which localized disturbances in a vertically oscillating long channel become instable. Modulated cross-waves with a carrier frequency close to natural are considered, and the channel is subjected to oscillations with the frequency shifted slightly below twice the natural value. The waves are described by the Miles equation. We also report numerical investigations into the instability of solitary wave disturbances for a range of controlling parameters.

MSC:
76E30 Nonlinear effects in hydrodynamic stability
76B25 Solitary waves for incompressible inviscid fluids
76M20 Finite difference methods applied to problems in fluid mechanics
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