  We investigate the propagation characteristics of electrostatic dust-acoustic
(DA) solitary waves and shocks in a strongly coupled dusty plasma consisting of
intertialess electrons and ions, and strongly coupled inertial charged dust
particles. A generalized viscoelastic hydrodynamic model with the effects of
electrostatic dust pressure associated with the strong coupling of dust
particles, and a quantum hydrodynamic model with the effects of quantum forces
associated with the Bohm potential and the exchange-correlation potential for
electrons and ions are considered. Both the linear and weakly nonlinear theory
of DA waves are studied by the derivation and analysis of dispersion relations
as well as Korteweg-de Vries (KdV) and KdV-Burgers (KdVB)-like equations. It is
shown that in the kinetic regime ($\omega\tau_m\gg1$, where $\omega$ is the
wave frequency and $\tau_m$ is the viscoelastic relaxtation time), the
amplitude of the DA solitary waves decays slowly with time with the effect of a
small amount of dust viscosity. However, the DA shock-like perturbations can be
excited in the hydrodynamic regime with $\omega\tau_m\ll1$. The analytical and
numerical solutions of the KdV and KdVB equations are also presented and
analyzed with the system parameters.
