The theory of dynamical (wake) potential behind a moving test charge in a weakly coupled dusty plasma is extended to that including of strong interaction between dust grains. Such strong interaction is included in the dielectric response function by a generalized hydrodynamic (GH) fluid model. It is shown that the strong interaction between dusts including the lattice spacing correction has a significant effect on the wake potential in dusty plasma. This may be used to investigate basic features of phase transition and possibility of lattice formation of dusty plasma.

Using the generalized viscoelastic fluid model, we derive the dielectric response function in a strongly coupled dusty magnetoplasma which reveals two different dust acoustic (DA) wave modes in the hydrodynamic and kinetic limits. The effects of the strong interaction of dust grains and the external magnetic on these DA modes, as well as on the shear wave are examined. It is found that both the real and imaginary parts of DA waves are significantly modified in strongly coupled dusty magnetoplasmas. The implications of our results to space and laboratory dusty plasmas are briefly discussed.

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