  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.
