Nonlinear interaction of four electrostatic waves in a plasma

Nonlinear wave–wave interactions in a system consisting of three Langmuir and one ion-sound waves are studied. Such a system can describe either a cascade of two decay instabilities or a modified decay instability. Special attention is paid to phases, which in the decay case exhibit chaotic synchronization under particular conditions when the system has an additional invariant. While mutual information suggests decoupling between amplitudes and phases, conditions for the standard random phase approximation are not fulfilled. Modified decay instability in the same system is clearly distinguished by smaller entropy and attractor’s dimension.