The coupling of two waves due to the presence of a third wave with large amplitude is studied. On the basis of simple model equations, the conditions for excitation of the first two waves are discussed for the following three cases: i) \(\omega_{1}+\omega_{2}{\risingdotseq}\omega_{0}\) and ω 1 , ω 2 are large compared with their frequency shift, ii) \(\omega_{1}{\ll}\omega_{2}{\lesssim}\omega_{0}\) and iii) \(\omega_{1}{\ll}\omega_{0}{\lesssim}\omega_{2}\), where ω 1 , ω 2 are the unperturbed frequencies of the two waves under consideration and ω 0 is the frequency of the incident large amplitude wave. In the first two cases, the excited wave is found oscillatory, while in the third it is found non-oscillatory. The threshold power of the incident wave for the onset of excitation, the frequency shift at the threshold and the growth rate above threshold are calculated in each case.

Parametric Excitation of Coupled Waves I. General Formulation