The quantum hydrodynamic model for plasmas is employed to study the dynamics of the nonlinear quantum dust acoustic ͑QDA͒ wave in a nonuniform quantum dusty plasma ͑QDP͒. Through the reductive perturbation technique, it is shown that the quantum hydrodynamical basic equations describing the nonlinear QDA waves yield a modified Korteweg-de Veries equation with slowly varying coefficients in the system inhomogeneity. Applying generalized expansion method, it is found that the system admits only rarefactive solitons. The properties of the solitons such as the velocity, the amplitude and the width of the nonlinear QDA waves are analyzed using appropriate choice for initial ion and electron density numbers. For the homogeneous QDP, no critical value is found. Because of the system inhomogeneity, a new criticality is found forcing with the usage of new stretching coordinates. A higher evolution equation with third-order nonlinearity is derived at the critical values. The solution of the latter equation admits rarefactive shock wave attached with an amplitude factor. The present investigations should be useful for researches on astrophysical plasmas as well as for ultra small micro-and nano-electronic devices.

The characteristics of the head-on collision (HOC) between two positron acoustic solitary waves (PASWs) in a four component electron-positron-ion (EPI) space plasma have been investigated theoretically, using the extended Poincaré-Lighthill-Kuo (PLK) method. The analytical phase shifts after the collision of the two solitary

The effect of nonthermal ions and variable dust charge on small-amplitude nonlinear dust-acoustic (DA) waves is investigated. It is found that both compressive and rarefactive solitons exist and depend on the nonthermal parameter a. Using a reductive perturbation theory, a Zakharov–Kuznetsov (ZK) equation is derived. At critical value of a, ac, a modified ZK equation with third- and fourth-order nonlinearities, is obtained. Depending on a, the solution of the evolution equation reveals whether there is coexistence of both compressive and rarefactive solitary waves or double layers (DLs) with the possibility of their two kinds. In addition, for certain plasma parameters, the solitary wave disappears and a DL is expected. The variation of dust charge number, wave velocity, and soliton amplitude and its width against system parameters is investigated for the DA solitary waves. It is shown that the incorporation of both the adiabatic dust-charge variation and the nonthermal distributed ions modifies significantly the nature of DA solitary waves and DA DLs. The findings of this investigation may be useful in understanding the ion acceleration mechanisms close to the Moon and also enhances our knowledge on pickup ions around unmagnetized bodies, such as comets, Mars, and Venus.

Nonlinear propagation of fast and slow magnetosonic perturbation modes in an ultrarelativistic, ultracold, degenerate (extremely dense) electron positron (EP) plasma (containing ultrarelativistic, ultracold, degenerate electron and positron fluids) has been investigated by the reductive perturbation method. The Alfvén wave velocity is modified due to the presence of the enthalpy correction in the fluid equations of motion. The degenerate EP plasma system (under consideration) supports the Korteweg-de Vries (KdV) solitons, which are associated with either fast or slow magnetosonic perturbation modes. It is found that the ultrarelativistic model leads to compressive (rarefactive) electromagnetic solitons corresponding to the fast (slow) wave mode. There are certain critical angles, θ(c), at which no soliton solution is found corresponding to the fast wave mode. For the slow mode, the magnetic-field intensity affects both the soliton amplitude and width. It is also illustrated that the basic features of the electromagnetic solitary structures, which are found to exist in such a degenerate EP plasma, are significantly modified by the effects of enthalpy correction, electron and positron degeneracy, magnetic-field strength, and the relativistic effect. The applications of the results in a pair-plasma medium, which occurs in many astrophysical objects (e.g., pulsars, white dwarfs, and neutron stars) are briefly discussed.

The ionization source model is considered, for the first time, to study the combined effects of trapped electrons, transverse perturbation, ion streaming velocity, and dust charge fluctuations on the propagation of dust-ion-acoustic solitons in dusty plasmas. The solitary waves are investigated through the derivation of the damped modified Kadomtsev–Petviashivili equation using the reductive perturbation method. Conditions for the formation of solitons as well as their properties are clearly explained. The relevance of our investigation to supernovae shells is also discussed.

The derivative expansion perturbation method is applied to a strongly coupled dusty plasma system consisting of negatively charged dust grains, electrons, and ions. The basic equations are reduced to a nonlinear Schrödinger type equation appropriate for describing the modulated dust acoustic (DA) waves. We have examined the modulation (in) stability and the dependence of the system physical parameters (angular frequency and group velocity) on the polarization force variation. Finally, the extended Poincaré-Lighthill-Kuo technique is employed to investigate the head-on collision (HoC) between two DA dark solitons. The analytical phase shifts and the trajectories of these dark solitons after the collision are derived. The numerical illustrations show that the polarization effect has strong influence on the nature of the phase shifts and the trajectories of the two DA dark solitons after collision.

The combined effects of trapped ion distribution, two-ion-temperature, dust charge fluctuation, and dust fluid temperature are incorporated in the study of nonlinear dust acoustic waves in an unmagnetized dusty plasma. It is found that, owing to the departure from the Boltzmann ion distribution to the trapped ion distribution, the dynamics of small but finite amplitude dust acoustic waves is governed by a modified Korteweg-de Vries equation. The latter admits a stationary dust acoustic solitary wave solution, which has stronger nonlinearity, smaller amplitude, wider width, and higher propagation velocity than that involving adiabatic ions. The effect of two-ion-temperature is found to provide the possibility for the coexistence of rarefactive and compressive dust acoustic solitary structures and double layers. Although the dust fluid temperature increases the amplitude of the small but finite amplitude solitary waves, the dust charge fluctuation does the opposite effect. The present investigation should help us to understand the salient features of the nonlinear dust acoustic waves that have been observed in a recent numerical simulation study.

Propagations of nonlinear dust acoustic (DA) solitary waves and shock waves in a nonuniform magnetized dusty plasma are investigated. The incorporation of the combined effects of nonthermally distributed ions, nonadiabatic dust charge fluctuation, and the inhomogeneity caused by nonuniform equilibrium values of particle density, charging variable, and particle potential on the waves leads to a significant modification to the nature of nonlinear DA solitary waves. The nonlinear wave evolution is governed by a modified Zakhavov-Kusnetsov-Burgers (MZKB) equation, whose coefficients are space dependent. Using a generalized expansion method, new solutions for the MZKB equation are obtained. The form of solutions consists of two parts; one of them is the amplitude factor and the other is a superposition of bell-shaped and kink-type shock waves. New solutions are classified into three categories. A type of the solution is determined depending on the nonthermal parameter. Findings in this investigation should be useful for understanding the ion acceleration mechanisms close to the Moon and also enhancing our knowledge on pickup ions around unmagnetized bodies, such as comets, Mars, and Venus, including medium inhomogeneities with nonadiabatic dust charging processes.