Nonlinear interaction of four electrostatic waves in a plasma

Nonlinear wave-wave interactions in a system consisting of three Langmuir a nd one ion-sound waves are studied. Such a system can describe either a cas cade of two decay instabilities or a modified decay instability. Special at tention is paid to phases, which in the decay case exhibit chaotic synchron ization under particular conditions when the system has an additional invar iant. While mutual information suggests decoupling between amplitudes and p hases, conditions for the standard random phase approximation are not fulfi lled. Modified decay instability in the same system is clearly distinguishe d by smaller entropy and attractor's dimension. (C) 2001 Published by Elsev ier Science B.V.