Dynamics of four coupled plasma waves to second order

General equations are derived for the interaction of four waves to second order (i.e. two triplets with two waves common to both). The solutions are analysed under various initial conditions and it is shown that the weaker triplet (as measured by the coupling constraints) is stabilized by the stronger one against explosive instabilities, whereas the converse does not happen. It is further found that under certain circumstances one of the common waves may act as a ‘catalyst’, remaining fixed in amplitude, while the other waves oscillate or even grow exponentially. This work extends the treatment of Karplyuk, Oraevskii & Pavlenko to include the possibility of negative energy waves.