Small-Amplitude Shock Waves and Double Layers in Dusty Plasmas with Opposite Polarity Charged Dust Grains¹

Abstract—Theoretical investigation is carried out for understanding the properties of nonlinear dust-acoustic (DA) waves in an unmagnetized dusty plasma whose constituents are massive, micron-sized, positive and negatively charged inertial dust grains along with $q$ (nonextensive) distributed electrons and ions. The reductive perturbation method is employed in order to derive two types of nonlinear dynamical equations, namely, Burgers equation and modified Gardner equation (Gardner equation with dissipative term). They are also numerically analyzed to investigate the basic features (viz., polarity, amplitude, width, etc.) of shock waves and double layers. It has been observed that the effects of nonextensivity, opposite polarity charged dust grains, and different dusty plasma parameters have significantly modified the fundamental properties of shock waves and double layers. The results of this investigation may be used for researches of the nonlinear wave propagation in laboratory and space plasmas.