In this paper, two mode-coupling analyses for the nonlinear excitation of the geodesic acoustic modes (GAMs) in tokamak plasmas by drift waves are presented. The first approach is a coherent parametric process, which leads to a three-wave resonant interaction. This investigation allows for the drift waves and the GAMs to have comparable scales. The second approach uses the wave-kinetic equations for the drift waves, which then couples to the GAMs. This requires that the GAM scale length be large compared to the wave packet associated with the drift waves. The resonance conditions for these two cases lead to specific predictions of the radial wave number of the excited GAMs.

The well known Jeans instability is studied for a viscoelastic, gravitational fluid using generalized hydrodynamic equations of motions. It is found that the threshold for the onset of instability appears at higher wavelengths in a viscoelastic medium. Elastic effects playing a role similar to thermal pressure are found to lower the growth rate of the gravitational instability. Such features may manifest themselves in matter consituting dense astrophysical objects.

The propagation of a nonlinear low-frequency mode in a strongly coupled dusty plasma is investigated using a generalized hydrodynamical model. For the well-known longitudinal dust acoustic mode a standard perturbative approach leads to a Korteweg-de Vries (KdV) soliton. The strong viscoelastic effect, however, introduced a nonlinear forcing and a linear damping in the KdV equation. This novel equation is solved analytically to show a competition between nonlinear forcing and dissipative damping. The physical consequence of such a solution is also sketched.

The geodesic acoustic modes ͑GAMs͒ are typically observed in the edge region of toroidal plasmas. Drift waves have been identified as a possible cause of excitation of GAMs by a resonant three wave parametric process. A nonlocal theory of excitation of these modes in inhomogeneous plasmas typical of the edge region of tokamaks is presented in this paper. The continuum GAM modes with coupling to the drift waves can create discrete "global" unstable eigenmodes localized in the edge "pedestal" region of the plasma. Multiple resonantly driven unstable radial eigenmodes can coexist on the edge pedestal.

Geodesic acoustic modes (GAMs) can be excited by mode coupling to primary modes such as the drift waves and ion temperature gradient modes in tokamak plasmas. Recent global numerical simulations of ion temperature gradient modes show excitation of GAMs and indicate that the radial wave-number of the excited GAMs scales inversely as the ion Larmor radius. Also the modes are excited dominantly in the edge region of the device. Furthermore there is a nonlinear downshift of the GAM frequency compared with the predicted linear mode frequency. The mode-coupling analysis presented in this paper provides an explanation of the scaling of the radial wave-number, the preferential excitation of GAMs in the outer half of the plasma and the nonlinear downshift of the frequency of GAMs.