The influence of strong correlations on low frequency collective modes
in a dusty plasma is investigated. The dust dynamics is modeled by th
e generalized hydrodynamics description. For the well known dust acous
tic mode, strong correlations lead to new dispersive corrections, an o
verall reduction of the frequency and phase velocity and the existence
of parameter regions where partial derivative omega/partial derivativ
e k<0. A novel result is the possibility of sustaining a low frequency
transverse mode-a dust shear mode-in which the correlation energy act
s as an effective bulk modulus. The influence of ion streaming and col
lisional interaction with a background of neutrals on the modes are al
so studied and it is shown that the longitudinal modes may be driven u
nstable by ion streaming. (C) 1998 American Institute of Physics. [S10
70-664X(98)03610-6].