  Wave-wave interaction in plasmas is a topic of important research since the
16th century. The formation of Langmuir solitons through the coupling of
high-frequency (hf) Langmuir and low-frequency (lf) ion-acoustic waves, is one
of the most interesting features in the context of turbulence in modern plasma
physics. Moreover, quantum plasmas, which are ubiquitous in ultrasmall
electronic devices, micromechanical systems as well as in dense astrophysical
environments are a topic of current research. In the light of notable interests
in such quantum plasmas, we present here a theoretical investigation on the
nonlinear interaction of quantum Langmuir waves (QLWs) and quantum ion-acoustic
waves (QIAWs), which are governed by the one-dimensional quantum Zakharov
equations (QZEs). It is shown that a transition to spatiotemporal chaos (STC)
occurs when the length scale of excitation of linear modes is larger than that
of the most unstable ones. Such length scale is, however, to be larger
(compared to the classical one) in presence of the quantum tunneling effect.
The latter induces strong QIAW emission leading to the occurrence of collision
and fusion among the patterns at an earlier time than the classical case.
Moreover, numerical simulation of the QZEs reveals that many solitary patterns
can be excited and saturated through the modulational instability (MI) of
unstable harmonic modes. In a longer time, these solitons are seen to appear in
the state of STC due to strong QIAW emission as well as by the collision and
fusion in stochastic motion. The energy in the system is thus strongly
redistributed, which may switch on the onset of Langmuir turbulence in quantum
plasmas.
