A rigorous theoretical investigation has been carried out on the propagation of nonplanar (cylindrical and spherical) dust-acoustic shock waves (DASHWs) in a collisionless four-component unmagnetized dusty plasmasystem containing massive, micron-sized, positively and negatively charged inertial dust grains along with $q$ (nonextensive) distributed electrons and ions. The well-known reductive perturbation technique has been used to derive the modified Burgers equation (which describes the shock wave properties) and its numerical solution. It has been observed that the effects of charged dust grains of opposite polarity, nonextensivity of electrons and ions, and different dusty plasma parameters have significantly modified the fundamental properties (viz., polarity, amplitude, width, etc.) of the shock waves. The properties of DASHWs in nonplanar geometry are found tobe significantly different from those in one-dimensional planar geometry. The findings of our results from this theoretical investigation may be useful in understanding the nonlinear features of localized electrostatic disturbancesin both space and laboratory dusty plasmas.

The nucleus-acoustic shockwaves (NASWs) propagating in a white dwarf plasma system, which contain non-relativistically or ultrarelativistically degenerate electrons, non-relativistically degenerate, viscous fluid of light nuclei, and immobile nuclei of heavy elements, have been theoretically investigated. We have used the reductive perturbation method, which is valid for small but finite-amplitude NASWs to derive the Burgers equation. The NASWs are, in fact, associated with the nucleus-acoustic (NA) waves in which the inertia is provided by the light nuclei, and restoring force is provided by the degenerate pressure of electrons. On the other hand, the stationary heavy nuclei participate only in maintaining the background charge neutrality condition at equilibrium. It is found that the viscous force acting in the fluid of light nuclei is a source of dissipation, and is responsible for the formation of NASWs. It is also observed that the basic features (polarity, amplitude, width, etc.) of the NASWs are significantly modified by the presence of heavy nuclei, and that NASWs are formed with either positive or negative potential depending on the values of the charge density of the heavy nuclei. The basic properties are also found to be significantly modified by the effects of ultrarelativistically degenerate electrons. The implications of our results in white dwarfs are briefly discussed.

The nonlinear propagation of dust-acoustic waves (DAWs) and associated dust-acoustic rogue waves (DARWs), which are governed by the nonlinear Schrödinger equation, is theoretically investigated in a four componentplasma medium containing inertial warm negatively charged dust grains and inertialess non-thermal distributed electrons as well as isothermal positrons and ions. The modulationally stable and unstable parametric regimes of DAWs are numerically studied for the plasma parameters. Furthermore, the effects of temperature ratios of ion-to-electron and ion-to-positron, and the number density of ion and dust grains on the DARWs are investigated. It is observed that physical parameters play very crucial roles in the formation of DARWs. These results may be useful in understanding the electrostatic excitations in dusty plasmas in space and laboratory situations.