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Temporal dynamics in the one-dimensional quantum Zakharov equations for plasmas

The temporal dynamics of the quantum Zakharov equations (QZEs) in one spatial dimension, which describes the nonlinear interaction of quantum Langmuir waves (QLWs) and quantum ion-acoustic waves (QIAWs) is revisited by considering their solution as a superposition of three interacting wave modes in Fourier space. Previous results in the literature are modified and rectified. Periodic, chaotic as well as hyperchaotic behaviors of the Fourier-mode amplitudes are identified by the analysis of Lyapunov exponent spectra and the power spectrum. The periodic route to chaos is explained through an one-parameter bifurcation analysis. The system is shown to be destabilized via a supercritical Hopf-bifurcation. The adiabatic limits of the fully spatio-temporal and reduced systems are compared from the viewpoint of integrability properties.