The interaction of three monochromatic waves (two positive energy longitudinal waves and one negative energy wave) is investigated. When only the first-order nonlinear interactions are considered, an explosive instability occurs. However, this instability is stabilized by the higher order nonlinear interactions. The matrix elements of the three-wave and the four-wave interactions in a magnetized plasma are calculated.
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Fukai et al. (1970) studied this question.
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