Exact propagating nonlinear singular disturbances in strongly coupled dusty plasmas

The nonlinear longitudinal response of a strongly coupled dusty plasma system is analytically investigated using the Generalized Hydrodynamic (GHD) model. It is shown that the Galilean invariant form of the model does not have soliton solutions, but can support a variety of nonlinear singular (yet conservative) solutions like shock structures of zero strength and propagating solutions with cusp like singularities. These novel entities should be detectable in numerical simulations and experiments studying large amplitude longitudinal excitations in such systems.