Longitudinal singular response of dusty plasma medium in weak and strong coupling limits

Abstract

The longitudinal response of a dusty plasma medium in both weak and strong coupling limits has been investigated in detail using analytic as well as numerical techniques. In particular, studies on singular response of the medium have been specifically investigated here. A proper Galilean invariant form of the generalized hydrodynamic fluid model has been adopted for the description of the dusty plasma medium. For weak non-linear response, analytic reductive perturbative approach has been adopted. It is well known that in the weak coupling regime for the dusty plasma medium, such an analysis leads to the Korteweg-de Vries equation (KdV) equation and predicts the existence of localized smooth soliton solutions. We show that the strongly coupled dust fluid with the correct Galilean invariant form does not follow the KdV paradigm. Instead, it reduces to the form of Hunter-Saxton equation, which does not permit soliton solutions. The system in this case displays singular response with both conservative as well as dissipative attributes. At arbitrary high amplitudes, the existence and spontaneous formation of sharply peaked cusp structures in both weak and strong coupling regimes has been demonstrated numerically.