Interaction of nonlinear low frequency structures in a polarized dusty plasma *

The polarization force in dusty plasma arises when the dust Debye sphere is polarized due to  interaction with the background plasma particles.The density inhomogeneity is the main cause of the polarization of the Debye sphere. Polarization force modifies the dynamics of dust, which in turns modifies characteristics of nonlinear structures. The interaction of dust-acoustic (DA) shock waves in a magnetized dusty plasma under the influence of nonextensively modified polarization force is investigated. The plasma model consists of negatively charged dust, Maxwellian electrons, nonextensive ions and polarization force. In this investigation, we have derived the expression of polarization force in the presence of nonextensive ions and illustrated the head-on collision between two DA shock waves. The extended Poincar\'{e}-Lighthill-Kuo method is employed to obtain the two sided Korteweg-de Vries-Burgers (KdVB) equations and phase shifts of two shock waves. The trajectories and phase shifts of negative potential dust-acoustic shock waves after collision are examined. The combined effects of various physical parameters such as polarization force, nonextensivity of ions, viscosity of dust, and magnetic field strength on the phase shifts of DA shock waves have been studied.