A generalized hydrodynamical model has been used to study low frequency modes in a strongly coupled, cold, magnetized dusty plasma. Such plasmas exhibit elastic properties due to strong correlations among dust particles and the tensile stresses imparted by the magnetic field. It has been shown that longitudinal compressional Alfven modes and elasticity modified transverse shear mode exist in such a medium. The features of these collective modes are established and discussed.

An analysis of the interaction between modes involving two species with different pressures in the presence of a static-neutralizing ion background is presented using a quantum hydrodynamic model. It is shown that quantum electron plasma waves can nonlinearly interact with quantum electron acoustic waves in a time scale much longer than electron plasma oscillation response time. A set of coupled nonlinear differential equations is obtained that is similar to the Zakharov equations but includes quantum correction terms. These equations are solved in a moving frame, showing that solitary-wave-like solutions may also be possible in quantum Zakharov equations. It is also shown that quantum effects can reduce the growth rate of the usual caviton instability. Possible applications of the theory are also outlined.