Abstract
A set of third-order equations describing the interactions between surface waves and interfacial waves is presented. The specific interaction studied is that of exact subharmonic resonance of two interfacial waves by a single surface wave. The coupled amplitude evolution equations are solved analytically in terms of Jacobian elliptic functions. Upon specification of the initial conditions, the minimum and maximum amplitudes attained by the surface and interfacial waves, along with the nonlinear interaction period, are obtained. The results from the third-order theory are contrasted with those from second-order theory and highlight the importance of the cubic interactions.
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