Effects of two-temperature electrons, external oblique magnetic field, and higher-order nonlinearity on dust acoustic solitary waves in a dusty plasma with vortex-like ion distribution

Nonlinear properties of the dust acoustic (DA) solitary waves in a dusty plasma consisting of negatively variable-charged dust particles, vortex-like distributed ions and two-temperature isothermal electrons are reported. A reductive perturbation theory has been used to derive a modified Korteweg-de Vries (mKdV) equation for the first-order perturbed potential and a linear inhomogeneous mKdV-type equation for the second-order perturbed potential. The renormalization method is used to obtain stationary solutions of these coupled equations. The modifications in the amplitude and width of the solitary wave structure due to the inclusion of two different types of isothermal electrons, external oblique magnetic field, higher-order nonlinearity, and vortex-like distributed ions are investigated. Also a method based on energy consideration was used to obtain the stability condition. Moreover, the numerical results are applied to investigate some nonlinear characteristics of the DA solitary waves.     

On dust ion acoustic solitary waves in collisional dusty plasmas with ionization effect

The propagation of solitary waves in an unmagnetized collisional dusty plasma consisting of a negatively charged dust fluid, positively charged ions, isothermal electrons, and background neutral particles is studied. The ionization, ion loss, ion–neutral, ion–dust, and dust–neutral collisions are considered. Applying a reductive perturbation theory, a damped Korteweg–de Vries (DKdV) equation is derived. On the other hand, at a critical phase velocity, the dynamics of solitary waves is governed by a damped modified Korteweg–de Vries (DMKdV) equation. The nonlinear properties of solitary waves in the two cases are discussed.     

Effect of dust polarity on dust ion-acoustic localized structures in a superthermal dusty plasma

The effects of dust polarity and superthermal electrons are incorporated in the study of dust ion-acoustic (DIA) solitary waves (SWs) as well double layers (DLs) in a dusty plasma containing warm adiabatic ions, superthermal electrons, and arbitrarily (positively or negatively) charged immobile dust. Based on the energy-like integral equation, a new relationship between the localized electrostatic disturbances and dust polarity is derived. It is shown that there exists rarefactive SWs and DLs with qualitatively different structures in a way that depends on the population of superthermal electrons. As the electrons evolve their thermodynamic equilibrium, the localized structures are found with larger amplitude. It is also found that their amplitude increases (decreases) with the increase in the negative (positive) dust number density.     

Interaction of ion beam with dust grains produces dust-acoustic solitary waves in Herbig-Haro objects

Properties of dust-acoustic solitary waves in a warm dusty plasma are analyzed by using the hydrodynamic model for massive dust grains, electrons, ions, and streaming ion beam. For this purpose, Korteweg-de Vries (KdV) equation for the first-order perturbed potential and linear inhomogeneous KdV-type equation for the second-order perturbed potential have been derived and their analytical solutions are presented. In order to show the characteristics of the dust-acoustic solitary waves are influenced by the plasma parameters, the relevant numerical analysis of the KdV and linear inhomogeneous KdV-type equations are obtained. The dust-acoustic solitary waves, as predicted here, may be associated with the nonlinear structures caused by the interaction of polar jets with the interstellar medium, which is known as Herbig-Haro objects.     

Effect of nonextensive electron and ion on dust acoustic rogue waves in dusty plasma of opposite polarity

Propagation of nonlinear dust-acoustic waves in a magnetized collisionless plasma having positively, negatively charged dust grains and nonextensive distributed electrons and ions has been investigated. A reductive perturbation method is used to obtain a nonlinear Korteweg-de Vries (KdV) equation describing the model. The dynamics of the modulational instability gives rise to the formation of rogue waves that is described by a nonlinear Schrödinger equation. The dependence of rogue waves profiles on positive and negative charged dust cyclotron frequencies, nonextensive parameters of electrons and ions is investigated numerically. The result of the present investigation may be applicable to some plasma environments, such as cometary tails and upper mesosphere.     

Critical density solitary waves structures in a hot dusty plasma with vortex-like ion distribution in phase space

The nonlinear properties of solitary waves structure in a hot dusty plasma consisting of isothermal hot electrons, non isothermal ions and high negatively charged massive dust grains, are reported. A modified Korteweg-de Vries equation (modified KdV), which admits a solitary waves solution for small but finite amplitude, is derived using a reductive perturbation theory. A nonisothermal ions distribution provides the possibility of coexistence of amplitude rarefactive as well as compressive solitary waves. On the other hand, consideration of a critical ions density gives a stationary solution of solitary waves and the dynamics of small but finite amplitude of solitary waves is governed by Korteweg-de Vries equation (KdV). The properties of solitary waves in the two cases are discussed.     

Higher-order Zakharov–Kuznetsov equation for dust-acoustic solitary waves with dust size distribution

Nonlinear propagating dust-acoustic solitary waves (DASWs) in a warm magnetized dusty plasma containing different size and mass negatively charged dust particles, isothermal electrons, high- and low-temperature ions are investigated. For this purpose, a reasonable normalization of the hydrodynamic and Poisson equations is used to derive the Zakharov–Kuznetsov (ZK) equation for the first-order perturbed potential. As the wave amplitude increases, the width and the velocity of the solitons deviate from the prediction of the ZK equation, i.e., the breakdown of the ZK approximation. To describe the soliton of larger amplitude, a linear inhomogeneous Zakharov-Kuznetsov-type (ZK-type) equation for the second-order perturbed potential is derived. Stationary solutions of both equations are obtained using the renormalization method. Numerically, the effect of power law distribution on the higher-order corrections is examined. It is found that the soliton amplitude in case of power law distribution is smaller than that of monosized dust grains. The higher-order corrections play a role to reduce the strength of the nonlinearity for power law distribution case. The relevance of the present investigation to Saturn's F-ring and laboratory experiment is discussed.     

Dust ion-acoustic solitary waves in a dusty plasma with arbitrarily charged dust and flat-trapped electrons

The properties of arbitrary amplitude dust ion-acoustic (DIA) solitary waves (SWs) in a dusty plasma containing warm adiabatic ions, electrons following flat-topped velocity distribution, and arbitrarily (positively or negatively) charged immobile dust is studied by the pseudo-potential approach. The effects of ion temperature, resonant electrons, and dust number density are found to significantly modify the basic features of the DIA-SWs as well modify the parametric regime for the existence of compressive DIA-SWs. The pseudo-potential for small but finite amplitude limit is also analytically analyzed.     

Superthermal effect of electrons on nonplanar dust-ion-acoustic solitary waves and double layers in a dusty plasma

The basic features of planar and nonplanar time-dependent dust-ion-acoustic (DIA) solitary waves (SWs) and double layers (DLs) have been studied in an unmagnetized dusty plasma system consisting of positively and negatively charged dust, Boltzmann distributed ions and superthermal electrons (represented by kappa distribution). Using the reductive perturbation technique (RPT) we have derived modified Gardner (MG) equation, which gives information beyond the Korteweg-de Vries (KdV) limits (corresponding to the vanishing of nonlinear coefficient of the KdV equation). It is seen that the properties of nonplanar DIA SWs and DLs are significantly differs as the value of spectral index kappa (κ) changes. The present investigation may have relevance in the study of propagation of DIA waves in space and laboratory plasmas.     

Solitary solution and energy for the Kadomstev–Petviashvili equation in two temperatures charged dusty grains

The nonlinear properties of small amplitude dust-acoustic solitary waves (DAWs) in a homogeneous unmagnetized plasma having electrons, singly charged ions, hot and cold dust species with Boltzmann distributions for electrons and ions have been investigated. A reductive perturbation method was employed to obtain the Kadomstev-Petviashvili (KP) equation. The effects of the presence of charged hot and cold dust grains on the nature of DAWs were discussed. Moreover, the energy of two temperatures charged dusty grains were computed. The present investigation can be of relevance to the electrostatic solitary structures observed in various space plasma environments.     

Dust ion-acoustic solitary and shock waves in a dusty plasma with non-thermal electrons

A theoretical investigation of the one dimensional dynamics of nonlinear electrostatic dust ion-acoustic (DIA) waves in an unmagnetized dusty plasma consisting of ion fluid, non-thermal electrons and fluctuating immobile dust particles has been made by the reductive perturbation technique. The basic features of DIA solitary and shock waves are studied by deriving the Korteweg-de Vries (KdV) and KdV Burger equations, respectively. It is shown that the special patterns of nonlinear electrostatic waves are significantly modified by the presence of the non-thermal electron component. In particular, the rarefactive solitary and shock structures are found with smaller amplitude in comparison to the isothermal case. The transition from DIA solitary to shock waves is also studied which is related to the contributions of the dispersive and dissipative terms. It is found that the dust charge fluctuation is a source of dissipation, and is responsible for the formation of the dust ion-acoustic shock waves. Furthermore, the dissipative effect becomes important and may prevail over that of dispersion as the population of non-thermal electrons present decreases. The present investigation may be of relevance to electrostatic solitary structures observed in many space dusty plasma, such as Saturn’s E-ring.     

Effects of dust charge fluctuations and deviations from isothermality of electrons on nonlinear dust ion-acoustic waves

The effects of dust charge fluctuations and deviations from isothermality of electrons are incorporated in the study of nonlinear dust ion-acoustic waves. Deviations from isothermality of electrons are included in this model as a result of nonlinear resonant interaction of the electrostatic wave potential with electrons during its evolution. The basic properties of stationary structures are studied by employing the reductive perturbation method, and conditions for the formation of small but finite amplitude dust ion-acoustic solitary waves in the space dusty plasma situations are clearly explained. It is shown that a more depletion of the background free electrons owing to the attachment of these electrons to the surface of the dust grains during the charging process can lead to the formation of solitary waves with smaller amplitude. Furthermore, effects of the dust charge fluctuation and deviations from isothermality of electrons show a non-uniform behavior for the amplitude of solitary waves in transition from the Boltzmann electron distribution to a trapped electron one. It is also found that the dust charge fluctuation caused by trapped as well as free electrons is a source of dissipation, and is responsible for the formation of the dust ion-acoustic shock waves.     

Dust-ion-acoustic solitary waves and their multi-dimensional instability in a magnetized nonthermal dusty electronegative plasma

A rigorous theoretical investigation has been made on multi-dimensional instability of obliquely propagating electrostatic dust-ion-acoustic (DIA) solitary structures in a magnetized dusty electronegative plasma which consists of Boltzmann electrons, nonthermal negative ions, cold mobile positive ions, and arbitrarily charged stationary dust. The Zakharov-Kuznetsov (ZK) equation is derived by the reductive perturbation method, and its solitary wave solution is analyzed for the study of the DIA solitary structures, which are found to exist in such a dusty plasma. The multi-dimensional instability of these solitary structures is also studied by the small-k (long wave-length plane wave) perturbation expansion technique. The combined effects of the external magnetic field, obliqueness, and nonthermal distribution of negative ions, which are found to significantly modify the basic properties of small but finite-amplitude DIA solitary waves, are examined. The external magnetic field and the propagation directions of both the nonlinear waves and their perturbation modes are found to play a very important role in changing the instability criterion and the growth rate of the unstable DIA solitary waves. The basic features (viz. speed, amplitude, width, instability, etc.) and the underlying physics of the DIA solitary waves, which are relevant to many astrophysical situations (especially, auroral plasma, Saturn’s E-ring and F-ring, Halley’s comet, etc.) and laboratory dusty plasma situations, are briefly discussed.     

Influence of arbitrarily charged dust and trapped electrons on propagation of localized dust ion-acoustic waves

A theoretical investigation is developed to study the existence, formation and basic properties of arbitrary amplitude dust ion-acoustic solitary potentials in a dusty plasma consisting of warm ions, trapped electrons and immobile negative (positive) dust particles. It is found a definite interval for the Mach number for which solitary waves exist and depend sensitively on the ion temperature and negative (positive) dust concentration. In addition, the effects of ion temperature, two oppositely charged dust species and resonant electrons on the shape of the solitary waves are also investigated extensively. For both cases of negative and positive dust grains, the effect of ion temperature is found to be destructive for the formation of localized structures. Further, the amplitude of the solitary structures decreases (increases) with the increase in the negative (positive) dust concentration.     

Effect of nonthermality of ions on the nature of dust acoustic waves in two temperatures charged dusty grains

Effect of nonthermality of ions on the propagation of dust-acoustic waves (DAWs) in unmagnetized plasma having electrons, singly charged ions, hot and cold dust grains have been investigated. The reductive perturbation method is employed to reduce the basic set of fluid equations to the Korteweg-de Vries (KdV) equation. Moreover, the energy of two temperatures charged dusty grains were computed. The present investigation can be of relevance to the electrostatic solitary structures observed in various space plasma environments.     

Investigation of non-isothermal electron effects on the dust acoustic waves in four components dusty plasma

The time fractional modified KdV, the so-called TFMKdV equation is solved to study the nonlinear propagation of the dust acoustic (DA) solitary waves in un-magnetized four components dusty plasma. This plasma consists of positively charged warm adiabatic dust, negatively charged cold dust, non-isothermal electrons and Maxwellian ions. The TFMKdV equation is derived by using semi-inverse and Agrawal’s method and solved by the Laplace Adomian decomposition method (LADM). The effects of the time fractional order (β), the ratio of dust to ion temperature (δ _d ), the time (τ), the mass and charge ratio (α), the non-isothermal parameter (γ) and wave velocity (v) on the DA solitary wave are studied. Our results show that the variations of the amplitude of DA solitary wave versus (γ) are in agreement with the results obtained previously. Moreover, the time fractional order plays a role of higher order perturbation in modulating the soliton shape. The achievements of this research for the DA solitary waves may be applicable in space plasma environments and laboratory plasmas.     

Nonlinear propagation of dust ion-acoustic waves in dusty multi-ion dense plasma

We have studied the nonlinear propagation of dust ion-acoustic (DIA) waves in a dusty multi-ion dense plasma (with the constituents being degenerate, either non-relativistic or ultra-relativistic) and the propagation of such waves have been investigated by the reductive perturbation method. From the stationary solution of the Korteweg de-Vries (K-dV) equation and Burgers’ equation the nonlinear waves (specially, solitary and shock waves) have been found to be formed in the dusty plasma system under consideration. It has shown that the basic features of these waves are significantly modified by both the positive and negative ions and dust number densities, the degenerate of the constituents. The implications of our results have been briefly discussed.     

Obliquely propagating electrostatistic solitary structures in a hot magnetized dusty plasma with vortex-like electron distribution

The nonlinear properties of solitary waves structure in a hot magnetized dusty plasma consisting of a negatively charged, extremely massive hot dust fluid, positively charged hot ion fluid and vortex-like distributed electrons, are reported. A modified Korteweg de Vries equation (mKdV) which admits a solitary wave solution for small but finite amplitude is derived using a reductive perturbation theory. The modifications in the amplitude and width of the solitary wave structures due to the inclusion of an external magnetic field and dust and ions temperature are investigated. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effects of nonthermal ions of distinct temperatures on dust acoustic shock waves in a dusty plasma

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.     

Evolution of ion-acoustic solitary waves in magnetized plasma contaminated with varying dust charged grains

Propagation of plasma-acoustic wave has been studied in magnetized plasma contaminated with dust charged grains. It has shown that, because of the configuration of magnetized plasma contaminated with dust charge fluctuation, pseudopotential method fails to derive nonlinear wave equation. We thus exercise an alternate approach to yield wave equation in the form of Sagdeev-like potential equation which enables the success to study the nonlinear waves. Again a modified mathematical formalism known as tanh-method has the merit to evaluate the soliton features in relation to its expectation in space. The method has its success in finding the solitary waves along with other exciting formation of shock-like wave, soliton radiation in soliton propagation. The results have more realistic interpretation in showing explicitly the interaction of magnetic field and impurity caused by dust charge variation.