A. A. Mamun

Cylindrical and spherical dust ion–acoustic solitary waves

The properties of cylindrical and spherical dust ion–acoustic solitary waves (DIASWs) in an unmagnetized dusty plasma, whose constituents are inertial ions, Boltzmann electrons, and stationary dust particles, are investigated by employing the reductive perturbation method. The modified Korteweg–de Vries equation is derived and its numerical solutions are obtained. It has been found that the properties of the DIASWs in a nonplanar cylindrical or spherical geometry differ from those in a planar one-dimensional geometry.

Solitons, shocks and vortices in dusty plasmas

Three important classes of nonlinear phenomena, namely solitons, shocks and vortices in dusty plasmas, have been discussed. The static and mobile charged dust grains have been considered in order to study all of these nonlinear phenomena. The effects of nonplanar geometry, dust grain charge fluctuations, dust fluid temperature, vortex-like ion distribution, strong dust correlation etc on the properties of dust ion-acoustic/dust-acoustic solitons have also been analysed. The implications of these theoretical investigations in experimental observations of soliton and shock formation in dusty plasmas are briefly discussed.

Spherical and cylindrical dust acoustic solitary waves

Abstract The nonlinear propagation of cylindrical and spherical dust acoustic (DA) waves in an unmagnetized dusty plasma is considered. By employing the reductive perturbation technique, a modified Korteweg–de Vries (K–dV) equation is derived from the dust continuity and momentum equations, Poissons equation as well as Boltzmann electrons and ions. Numerical solutions of the modified K–dV equation are obtained. It has been found that the propagation characteristics of the cylindrical and spherical DA solitary waves significantly differ from those of one-dimensional DA solitary waves.

Obliquely propagating electron-acoustic solitary waves

A theoretical investigation is carried out for understanding the properties of obliquely propagating electron-acoustic solitary waves (EASWs) in a magnetized plasma whose constituents are a cold magnetized electron fluid, hot electrons obeying a vortex-like distribution, and stationary ions. It is found that the present plasma model supports EASWs having a positive potential, which corresponds to a dip (hump) in the cold (hot) electron number density. The effects of the external magnetic field and the obliqueness are found to significantly change the basic properties (viz. the amplitude and the width) of the EASWs. The present investigation can be of relevance to the electrostatic solitary structures observed in various space plasma environments (viz. the cusp of the terrestrial magnetosphere, the geomagnetic tail, the auroral regions, etc.).

Dust-acoustic shocks in a strongly coupled dusty plasma

It is shown that the nonlinear propagation of the dust-acoustic waves in a strongly coupled dusty plasma is governed by a Korteweg-de Vries-Burgers (K-dV-Burgers) equation. The latter is derived from a set of generalized hydrodynamic equations for strongly correlated dust grains, as well as the Boltzmann distribution for electrons and ions. Possible stationary solutions of the K-dV-Burgers equation are represented in terms of monotonic/oscillatory shock profiles.

The role of dust charge fluctuations on nonlinear dust ion-acoustic waves

The nonlinear propagation of the dust ion-acoustic waves has been investigated accounting for the charge fluctuation dynamics of stationary dust grains in an unmagnetized dusty plasma. The Korteweg-de Vries equation, as well as the Korteweg-de Vries-Burgers equation, are derived by employing the reductive perturbation method. It has been shown that dust charge fluctuations produce a dissipation which is responsible for shock waves. Conditions for the formation of dust ion-acoustic solitary and shock waves as well as their properties are clearly explained. The implications of our investigations to both space and laboratory dusty plasmas are discussed.

Solitary waves in an ultrarelativistic degenerate dense plasma

Solitary waves in an ultrarelativistic degenerate dense plasma have been investigated by the reductive perturbation method. The modified Korteweg–de Vries equation has been derived and its numerical solutions have been analyzed to identify the basic features of spherical electrostatic solitary structures that may form in such a degenerate dense plasma. The implications of our results in compact astrophysical objects, particularly in white dwarfs, have been briefly discussed.

Charging of dust grains in a plasma with negative ions

The role of negative ions on the charging of dust grains in a plasma is examined. Two models for negative ion distributions are considered. These are streaming negative ions and Boltzmannian negative ions. It is found that the effects of the negative ion number density, negative ion charge, and negative ion streaming speed significantly affect the dust grain surface potential or the dust grain charge.

Nonlinear propagation of dust-acoustic waves in a magnetized dusty plasma with vortex-like ion distribution

A theoretical investigation has been made of the nonlinear propagation of dust-acoustic waves in a magnetized three-component dusty plasma consisting of a negatively charged dust fluid, free electrons and vortex-like distributed ions. It is found that, owing to the departure from the Boltzmann ion distribution to a vortex-like one, the dynamics of small- but finite-amplitude dust-acoustic waves in a magnetized dusty plasma is governed by the modified Korteweg–de Vries equation. The latter admits a stationary dust-acoustic solitary-wave solution that has larger amplitude, smaller width and higher propagation velocity than that involving adiabatic ions. The effects of external magnetic field, trapped ions and free electrons on the properties of these dust-acoustic solitary waves are briefly discussed.

Instability of Obliquely Propagating Electrostatic Solitary Waves in a Magnetized Nonthermal Dusty Plasma

A theoretical investigation has been made of instability of obliquely propagating electrostatic solitary structures in a magnetized three-component dusty plasma, which consists of a negatively charged dust fluid, Blotzmann distributed electrons, and free as well as fast ions. The Zakharov–Kuznetsov equation for these electrostatic solitary structures that exist in this plasma system is derived and their three dimensional instability is studied by the small-k (long-wavelength plane wave) perturbation expansion method. The instability criterion and its growth rate depending on the magnetic field and the propagation directions of the solitary waves are discussed. The implications of these results to some space and astrophysical plasma situations are briefly mentioned.