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The method of averaging in the study of nonlinear oscillations is applied to the problem of resonant wave‐wave interaction of a nonlinear dispersive wave system. The simplicity and directness of the method make it possible to study rather general and complex systems. Two examples are treated, one is posed as an initial value problem and the other as a boundary value problem. The second example deals with the acoustic‐gravity wave system in the atmosphere. It is found that resonant condition can be satisfied for the three‐wave system for which one of the waves is the zero frequency gravity wave. Through resonant interaction, the other two waves become trapped. The trapping depth is plotted for typical atmospheric parameters.
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Yeh et al. (1970) studied this question.
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