A novel hyperchaos in the quantum Zakharov system for plasmas

The nonlinear interaction of quantum Langmuir waves (QLWs) and quantum ion-acoustic waves (QIAWs) described by the one-dimensional quantum Zakharov equations (QZEs) is reinvestigated. A Galerkin type approximation is used to reduce the QZS to a simplified system (SS) of nonlinear ordinary differential equations which governs the temporal behaviors of the slowly varying envelope of the high-frequency electric field and the low frequency density fluctuation. This SS is then shown to establish the coexistence of novel hyperchaotic attractors, whose appearance is explained by means of the analysis of Lyapunov exponent spectra as well as the Kaplan–Yorke dimension. The system has an equilibrium point which depends parametrically on the nondimensional quantum parameter (H)(H) proportional to quantum diffraction, the plasmon number (N)(N) and the wave number of perturbation (α)(α), and which can evolve into periodic, quasi-periodic, chaotic and hyperchaotic states in both semiclassical and quantum cases.