Parametric Excitation of Coupled Waves I. General Formulation

抄録

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) ω₁+ω₂\ isingdotseqω₀ and ω₁, ω₂ are large compared with their frequency shift, ii) ω₁<<ω₂\lesssimω₀ and iii) ω₁<<ω₀\lesssimω₂, where ω₁, ω₂ are the unperturbed frequencies of the two waves under consideration and ω₀ 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.