Quantum Zakharov equations are obtained to describe the nonlinear interaction between quantum Langmuir waves and quantum ion-acoustic waves. These quantum Zakharov equations are applied to two model cases, namely the four-wave interaction and the decay instability. In the case of the four-wave instability, sufficiently large quantum effects tend to suppress the instability.For the decay instability, the quantum Zakharov equations lead to results similar to those of the classical decay instability except for quantum correction terms in the dispersion relations. Some considerations regarding the nonlinear aspects of the quantum Zakharov equations are also offered.

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The nonlinear dynamics of a finite-amplitude Alfvén wave in a dispersive modulational regime is analysed. Use is made of a conservative model to show that turbulence may arise via deterministic chaos. The behaviour of the system is studied as one varies the initial amplitude of the pump Alfvén wave, the dispersion parameter and the plasma parameter β.