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The basic characteristics of dust-acoustic (DA) shock waves (DASHWs) in self-gravitating dusty plasmas containing massive dust of opposite polarity, trapped ions, and Boltzmann electrons has been studied. The reductive perturbation technique has been employed to derive standard modified Burgers equation (mBE). The basic properties (viz., amplitude, width, and speed) of small but finite-amplitude DASHWs are significantly modified by the combined effects of positively and negatively charged dust component, self-gravitational force, and trapped ions. The implication of our investigation can be very effective for understanding and studying the nonlinear characteristics of the DA waves (DAWs) in laboratory and space dusty plasmas.

The propagation of dust-acoustic (DA) shock waves (SWs) is studied in a four-component dusty plasma system containing viscous dust fluids of opposite polarity, Schamel distributed ions and Boltzmann distributed electrons. The reductive perturbation method is employed to derive a modified Burgers equation which gives rise to the DA shock waves with stronger nonlinearity. The viscous force acting in the dust fluids is identified as a source of dissipation, and is responsible for the formation of the DA shock waves. The basic characteristics (viz., speed, amplitude, width) of the DA shock waves are found to be significantly modified by the combined effects of opposite polarity dust fluids and trapped ions. The applications of this investigation in different space plasma environments and laboratory devices are pinpointed.

A rigorous theoretical investigation has been made on dust-acoustic (DA) shock structures in an unmagnetized dusty plasma system whose constituents are negatively charged cold mobile dust fluid, electrons following Boltzmann distribution, and positively charged ions of two distinct temperatures following nonextensive ( $q$ ) and nonthermal distributions, respectively. In this paper, the Burgers’ equation has been derived by employing reductive perturbation technique which is valid for small but finite amplitude limit. It is observed that both the nonextensive and nonthermal ions of two distinct temperatures and dust kinematic viscosity significantly modify the basic properties (amplitudes, width, and polarities) of the DA shockwaves (DASHWs). The effects of low (high) temperature ions following nonextensive (nonthermal) and dust kinematic viscosity on DASHWs are examined both analytically and numerically. The implications of these results to some astrophysical environments and space plasmas (e.g., stellar polytropes, peculiar velocity distributions of galaxies, and collisionless thermal plasma), and laboratory dusty plasma systems are briefly mentioned.

The properties of dust-ion-acoustic Gardner double layers (DIA GDLs) in an unmagnetized dusty plasma, whose constituents are negatively-charged stationary dust, inertial ions, and Boltzmann electrons of two distinct temperatures, are rigorously investigated by employing the reductive perturbation method: Gardner approach. The standard Gardner equation is derived, and its double layer (DL) solution is obtained. It has been shown that the properties of the DIA GDLs are significantly modified by some plasma parameters (viz. σ=T e1/T e2, μ e1=n e10/n i0, and μ e2=n e20/n i0, where T e1 (T e2) is the cold (hot) electron temperature, n e10 (n e20) is the cold (hot) electron number density at equilibrium, and n i0 is the ion number density at equilibrium). The implications of our investigation in understanding the basic features of nonlinear electrostatic perturbations observed in many space plasma systems and laboratory devices are briefly discussed.

The effects of nonextensivity and nonthermality of ions of two distinct temperatures on dustacoustic Gardner solitons (DAGSs) in an unmagnetized dusty plasma system are investigated theoretically. The constituents of the dusty plasma under consideration are negatively charged mobile dust fluid, Boltzmann-distributed electrons, and ions of two distinct temperatures following nonextensive (q) and nonthermal distributions, respectively. The Korteweg-de Vries (KdV), modified KdV, and Gardner equations are derived by using the reductive perturbation technique, and thereby their characteristic features are compared. It is observed that both the nonextensive and nonthermal ions significantly modify the basic properties and polarities of dust-acoustic solitary waves. The present investigation may be of relevance to space and laboratory dusty plasma systems.

Propagation of the dust-acoustic shock waves (DASWs) in a dusty plasma containing arbitrarily charged dust, positive and negative ions following nonthermal (Cairn’s) distribution, and electrons following q-(nonextensive) distribution, has been investigated. The reductive perturbation technique is used to derive the Burgers equation for dust’s fluid dynamics. The basic features (viz. polarity, amplitude, speed, etc.) of DASWs are found to be significantly modified due to the effects of arbitrarily charged dust, number density and temperatures of heavier/lighter ions, nonextensive electrons, and dust kinematic viscosity. The present investigation can be very effective for understanding the nonlinear characteristics of the DASWs in space and laboratory dusty plasmas.

The fundamental properties of cylindrical and spherical dust-acoustic (DA) waves in dusty plasmas with consisting of negatively charged mobile dust, two populations of nonthermal ions with distinct temperatures, and Boltzmann-distributed electrons, are rigorously investigated both theoretically and analytically. The modified Gardner (mG) equation is derived by using the reductive perturbation method. The basic features of nonplanar DA modified Gardner solitons (mGSs) are analyzed by using numerical solutions of the mG equation. The nature and the basic characteristics of the mGSs are found to be significantly modified by the existence of two-temperature nonthermal ions. The implications of our investigations in understanding the nonlinear electrostatic perturbations observed in some astrophysical and space plasmas, where distinct-temperature nonthermal ions can significantly modify the wave dynamics, are briefly discussed in this current analysis.

The nonlinear propagation of dust acoustic (DA) waves in an unmagnetized dusty plasma system consisting of negatively charged mobile dust fluid, Boltzmann distributed electrons, and two-temperature nonthermally distributed ions, is rigorously investigated. The reductive perturbation method has been employed to derive the Burgers equation. The hydrodynamic equation for inertial dust grains has been used to derive the Burgers equation. The effects of two temperature nonthermally distributed ions and dust kinematic viscosity, which are found to significantly modify the basic features of DA shock waves, are briefly discussed. Our present investigation can be effectively utilized in many astrophysical situations (e.g. satellite or spacecraft observations, Saturn’s E ring, etc.), which are discussed briefly in this analysis.

The nonlinear propagation characteristics of cylindrical and spherical shock waves in an unmagnetized dusty plasma comprising of inertial negative dust, Boltzmann electrons, and ions with two distinct temperatures, are rigorously investigated by deriving the modified Burgers (mB) equation. Later, the nonplanar KdV-Burgers (nKdVB) equation is derived to show the presence of dispersive and dissipative effects on nonlinear waves. The standard reductive perturbation method is employed to derive the mB and nKdVB equations. The basic features of nonplanar dust-acoustic (DA) waves (viz. amplitude, profile structure, etc.) are discussed. The present analysis can play important role to understand the basic features of nonlinear electrostatic waves in astrophysical plasmas.

The nonlinear propagation characteristics of shock waves in a non-planar (cylindrical and spherical) two-ion-temperature unmagnetized dusty plasma, whose constituents are inertial negative dust, Boltzmann electrons and ions with two distinct temperatures, are investigated by deriving the modified Burgers (mB) equation. The standard reductive perturbation method is employed to derive the mB equation. The basic features of non-planar dust-acoustic (DA) shock waves (viz. amplitude, width, profile structure) are analyzed. It has been found that the propagation characteristics of non-planar DA shock waves significantly differ from those of planar ones.

A rigorous theoretical investigation has been performed on dust-acoustic (DA) solitary structures in an unmagnetized dusty plasma, consisting of negatively charged mobile dust grains, Boltzmann distributed electrons, and nonthermally distributed ions of two distinct temperatures. The Korteweg-de Vries (K-dV), modified K-dV (mK-dV) and Gardner equations, and their solitary waves (SWs) and double layer (DL) (in case of Gardner equation) solutions are derived by using the reductive perturbation technique. The basic features of the DA Gardner solitons (GSs) and DLs are studied analytically as well as numerically. It has been observed that the GSs significantly differ from K-dV and mK-dV solitons, and only positive potential DLs exist in the system. It is also studied that two-temperature nonthermal ions significantly modify the nature and basic properties of the DA SWs. The present investigation can be very effective for understanding and studying the nonlinear characteristics of the DA waves in laboratory and space dusty plasmas.