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Faraday resonance: asymptotic theory of surface waves. (English) Zbl 1194.76027
Summary: Some questions of a theory of regular surface waves in vertically oscillating rectangular tanks are treated. The wave processes considered to be described by the well-known Miles equation. The classification of possible crest-forms of permanent waves of small amplitude is given for values of the parameters close to the critical curve. We find families of periodic waves of two types, quasi-periodic waves, solitary waves and solitary waves with non-decreasing oscillations at infinity. The asymptotic form of a “two-soliton” solution, describing the interaction of two solitary waves for low amplitudes of an external force, is also presented.

MSC:
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35Q51 Soliton equations
76B25 Solitary waves for incompressible inviscid fluids
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