The impacts of dust size distribution on the head-on collision of quantum dust-acoustic solitary waves in ultradense astrophysical objects

The head-on collision between two quantum dust-acoustic solitary waves (QDASWs) in ultradense astrophysical objects has been investigated theoretically using the extended Poincaré-Lighthill-Kuo (PLK) method. The Korteweg-de Vries equations and the analytical phase shifts after the head-on collision of the two QDASWs in quantum dusty plasmas are obtained. Numerically, the obtained results demonstrate that the dust size distribution, the quantum corrections of diffraction and the temperatures of electrons and ions have strong effects on the nature of the phase shifts and the trajectories of the two QDASWs after collision.     

On existence conditions of dust-acoustic solitary waves in a plasma with positively charged dust

Dust acoustic (DA) solitary wave existence conditions are investigated for positively charged dust particles in the presence of nonthermal electrons. Once Sagdeev pseudo-potential derived through fluid equations, for large amplitude DA waves, the lower limit on Mach number is calculated analytically using the necessary condition for the solitary waves existence. The double layers conditions provides the upper limit on Mach number. This allowed us to numerically investigate the effect of the temperature, density and nonthermal parameters on the solitary waves’ characteristics. The present study is devoted to a complex plasma subject to ultraviolet radiations such as the one in the lower earth’s ionosphere.     

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.     

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.     

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 ion kinematic viscosity on large amplitude dust ion acoustic solitary waves

Nonlinear dust ion acoustic solitary waves (DIASW) in dusty plasma are studied incorporating kinematic viscosity, using Sagdeev’s pseudopotential approach. The effects of kinematic viscosity and the nonextensive parameter q on the features of DIASW are investigated in some detail.     

Head on collision of dust ion acoustic solitary waves in magnetized quantum dusty plasmas

The Head on collision of dust ion acoustic solitary waves (DIASWs) in a magnetized quantum dusty plasma is investigated. Two sides Korteweg-de Vries (KdV) equations are obtained, the analytical phase shifts and the trajectories after the head-on collision of two DIASWs in a three species quantum dusty plasma are derive by using the extended version of Poincaré-Lighthill-Kuo (PLK) method. It is observed that the phase shifts are significantly affected by the quantum parameters like quantum diffraction, the ion cyclotron frequency and the ratio of the densities of electrons to ions.     

Interaction of cylindrical and spherical ion acoustic solitary waves with superthermal electrons and positrons

Interaction of nonplanar ion acoustic solitary waves is an important source of information to study the nature and characteristics of ion acoustic solitary waves (IASWs) structures. The head-on collision between two cylindrical/spherical IASWs in un-magnetized plasmas comprising with inertial ions, superthermal electrons and positrons is investigated by using the extended version of Poincaré-Lighthill-Kuo (PLK) perturbation method. It has been shown numerically that how the interactions are taking place in cylindrical and spherical geometry. The nonplanar geometry modified analytical phase shifts following the head-on collision are derived. The effects of the superthermal electrons and positrons on the phase shift are studied. It is shown that the properties of the interaction IASWs in different geometry are very different.     

Arbitrary amplitude dust acoustic solitary waves in an electron-depleted dusty plasma with two high energy-tail ion distributions

Arbitrary amplitude dust acoustic waves (DAW’s) in two high energy-tail ion distributions are investigated. The electron number density has been assumed sufficiently depleted during the charging of the dust grains, on account of the attachment of the background plasma electrons on the surface of the dust grains. Our results reveal that under certain conditions, DA solitary waves with either negative or positive potential may be admitted. The high degree of suprathermalization of the relatively low temperature ion component favors the development of compressive localized structures. This behavior is preserved to a large extent in the small but finite amplitude regime. This means that the presence of additional relatively low temperature suprathermal ions does not only significantly modify the basic properties of DA structures, but also causes the existence of positive solitary potentials. This feature is completely new in a dusty plasma with two suprathermal ion components with widely disparate temperatures. Our results may be relevant to a number of space dusty plasma systems, particularly, the Saturn’s F-ring where electron depletion and suprathermality are thought to come into play.     

Oblique collision effects on nonlinear quantum dust-acoustic solitary waves in magnetized dense dusty plasmas

The oblique collision of nonlinear quantum dust-acoustic (NQDA) solitary waves in a three-dimensional (3D) magnetized dense dusty plasma is investigated. Furthermore, two coupled Kortwege–de Vries equations for describing our model and the analytical phase shifts after the oblique collision of two NQDA solitary waves are derived using the extended Poincaré–Lighthill–Kuo (PLK) method. The modification in the phase shift and the trajectory of the NQDA solitary waves structures due to the inclusion of oblique collision and external magnetic field are discussed numerically. The numerical results are applied to high density astrophysical situations such as in superdense white dwarfs.     

Dust acoustic solitary and shock waves in coupled dusty plasmas with variable dust charge and vortex-like ion distribution

The modified Kodomtsev-Petviashvili-Burger (mKP-Burger) and Kodomtsev-Petviashvili-Burger equations are derived in strongly coupled dusty plasmas containing iso-nonthermal ions; Boltzmann distributed electrons and variable dust charge. We use reductive perturbation method and discuss on solitary waves and shock waves solutions of these equations.     

Interaction of relativistic dust grains with the solar radiation field

The effects of the solar radiation field on the propagation of relativistic dust grains are evaluated. It is concluded that relativistic iron grains with energies 10¹⁹ eV will melt in the solar radiation field before they reach the Earth's orbit around the Sun. However iron grains with lower energies will reach the Earth's orbit but grains travelling from the direction of the Sun will melt. This directional anisotropy or fingerprint may be used to search for relativistic dust grains in the primary cosmic rays. The fact that no significant solar system anisotropy has been detected places constraints on the hypothesis that the initiating particles of the extensive air showers are relativistic iron grains.     

Influence of suprathermality on the obliquely propagating dust-acoustic solitary waves in a magnetized dusty plasma

Dust-acoustic (DA) solitary waves are investigated in a magnetized dusty plasma comprising cold dust fluid and kappa-distributed ions and/or electrons. The influence of suprathermal particles, obliqueness, and ion temperature on the DA solitary waves is investigated. We find that only negative DA solitary waves will be excited in this model. Also it is shown that the amplitude of the DA solitary wave decreases with deviation of electrons or ions from Maxwellian distribution via decrease of κ _e or κ _i . The effect of the temperature of the ion decreases with the amplitude and steepness of the solitary wave front.     

Bifurcations of dust acoustic solitary waves and periodic waves in an unmagnetized plasma with nonextensive ions

Bifurcations of dust acoustic solitary waves and periodic waves in an unmagnetized plasma with q-nonextensive velocity distributed ions are studied through non-perturbative approach. Basic equations are reduced to an ordinary differential equation involving electrostatic potential. After that by applying the bifurcation theory of planar dynamical systems to this equation, we have proved the existence of solitary wave solutions and periodic wave solutions. Two exact solutions of the above waves are derived depending on the parameters. From the solitary wave solution and periodic wave solution, the effect of the parameter (q) is studied on characteristics of dust acoustic solitary waves and periodic waves. The parameter (q) significantly influence the characteristics of dust acoustic solitary and periodic structures.     

Nonplanar ion acoustic solitary waves with superthermal electrons and positrons

The properties of cylindrical and spherical ion acoustic solitary waves (IASWs) are investigated in a three-component unmagnetized, collisionless plasma consisting of warm ion fluid and superthermally distributed electrons and positrons in a nonplanar cylindrical or spherical geometry. Using the reductive perturbation technique, the nonplanar cylindrical and spherical Korteweg-de Vries (KdV) equations are derived. The effects of spectral index of electron and positron, and other plasma parameters are studied. It is found that both negative as well as positive solitary potential structures are formed in nonplanar geometries. The numerical solution shows that amplitude of the soliton is large in spherical geometry in comparison with cylindrical geometry. Numerical results indicate that the amplitude of the soliton is large in spherical geometry in comparison with cylindrical geometry.     

Effects of two-temperature electrons, external oblique magnetic field, concentration of charged dust grains and higher-order nonlinearity on dust ion-acoustic solitary waves in Saturn's E-ring

The purpose of the present work is to investigate some nonlinear properties of the dust ion-acoustic (DIA) solitary waves in a four-component hot-magnetized dusty plasma consisting of charged dust grains, positively charged ions and two-temperature isothermal electrons. Applying a reductive perturbation theory, a nonlinear Korteweg-de Vries (KdV) equation for the first-order perturbed potential and a linear inhomogeneous KdV-type equation for the second-order perturbed potentials are derived. Stationary solutions of these coupled equations are obtained using a renormalization method. A method based on energy consideration is used to obtain a condition for stable solitons. The effects of two different types of isothermal electrons, external oblique magnetic field, concentration of negatively (positively) charged dust grains and higher-order nonlinearity on the nature of the DIA solitary waves are discussed. The numerical results are applied to Saturn's E-ring.     

Formation of dust ion-acoustic solitary waves in a dusty plasma with two-temperature trapped electrons

We look for particular solutions to the restricted three-body problem where the bodies are allowed to either lose or gain mass to or from a static atmosphere. In the case that all the masses are proportional to the same function of time, we find analogous solution to the five stationary solutions of the usual restricted problem of constant masses: the three collinear and the two triangular solutions, but now the relative distance of the bodies changes with time at the same rate. Under some restrictions, there are also coplanar, infinitely remote and ring solutions.     

Arbitrary amplitude dust-acoustic double-layers in a warm dusty plasma with suprathermal electrons, two-temperature thermal ions, and drifting dust grains

Arbitrary amplitude dust-acoustic double-layers (DA-DLs) in a plasma with suprathermal electrons, two-temperature thermal ions, and warm drifting dust grains are investigated. Our results reveal that the spatial patterns of the DA-DLs are affected by the degree of the electron suprathermality. The electron thermalization involves a decrease of the cold ion component density, for the existence of localized DA-DLs. An increase of the dust drift velocity requires a decrease of κ (the electron spectral index), for the onset of dust-acoustic double-layers. An increase of the Mach number M leads to an increase of the DL amplitude as well as the corresponding electron spectral index for which the DL occurs.     

Two-soliton solution of ion acoustic solitary waves in nonplanar geometry

The nonlinear wave structures of ion acoustic waves (IAWs) in an unmagnetized plasma consisting of superthermal electrons and warm ions are studied in bounded nonplanar geometry. Using reductive perturbation technique we have derived cylindrical and spherical Korteweg-de Vries (KdV) equations for IAWs to study the propagation of two-solitons. The presence of superthermally distributed electrons is shown to influence the propagation of two-solitons in nonplanar geometry.