Dust Acoustic Solitary Waves Research Articles

Analysis of Solution of Damped Modified-KdV Equation on Dust-Ion-Acoustic Wave in Presence of Superthermal Electrons

Nonlinear propagation of dust-ion-acoustic (DIA) waves in an unmagnetized collisional dusty plasma consisting of superthermal electrons, mobile ions and immobile negative dust particles have been investigated by employing the standard reductive perturbation technique. An analytical solution of the damped Korteweg–de Vries (KdV) equation is derived and the effects of superthermal electrons characterized by the parameter κ and dust-ion collision frequency $${{\nu }_{{{\text{id}}}}}$$ are found to modify the properties of the DIA solitary waves. In particular, it has been found that the presence of the superthermal electrons increases the amplitude and also the width of the nonlinear DIA wave. The variation of the amplitude and the width of the DIA wave have been found to be dependent on time. A parametric study of the variation of the electrostatic potential, amplitude, and width of the solitary wave is presented in this investigation.

Quantum effects in bi-dust plasmas

In this paper a theoretical approach has been carried out using a fluid model on a bi-dust plasma which consist of two dusts negative charged different particles in an electron–ion plasma. In such system, this fluid model describe a dense strong coupled heavy dust grain together with a weak coupled light dusty particle. The bulk is immersed in a system of electrons and ions dominated by a Thomas–Fermi density distribution, where interaction and propagation of solitary dust acoustic solitary waves will be analyzed. This investigation will be carried out for arbitrary amplitude of solitary dust acoustic waves. These are originated through the presence of both dust grains in the plasma system. Therefore, it is used a set of fluid equation which determine general expressions for the concentrations of different dust particles. The onset of the Sagdeev method is then employed in order to look for influence of the light component on the quantum system. In this way there is an increasing or decreasing in the Sagdeev potential. This is a quantum effect phenomena.

Effect of polarization and charge gradient forces on the dust acoustic solitary waves

The propagation of dust acoustic solitary waves (DASWs) in collisionless and unmagnetized plasma is investigated taking into account the effect of polarization and charge gradient forces. A Korteweg–de Vries equation and its stationary localized solution are obtained. Numerically, it is found that polarization force and charge gradient force have opposite effects on the amplitude and width of DASWs, i.e. polarization effect leads to an increase in the amplitude and a decrease in the width of DASWs, In contrast, the charge gradient effect enhances the amplitude of DASWs and weakens its width.

Ion-acoustic solitary wave solutions of nonlinear damped Korteweg–de Vries and damped modified Korteweg–de Vries dynamical equations

By using the reductive perturbation technique, the nonlinear dust ion-acoustic solitary wave models of the damped Korteweg–de Vries (D-KdV) and modified damped Korteweg–de Vries (D-mKdV) equations are formulated. We constructed the more general and new solitary wave solutions of nonlinear damped KdV and damped mKdV equations by using the modified mathematical technique. These obtained solutions are more useful in the development of quantum plasma, dynamics of solitons, dynamics of adiabatic parameters, dynamics of fluid and problems of biomedical, industrial phenomena. The new solutions are obtained in the shape of dark solitons, bright solitons, traveling wave and kink and anti-kink wave solitons. We show the physical structure of new solutions by two and three-dimensions graphical to know the physical interpretation of different structure of dust ion-acoustic solitary wave. The calculations show that this new technique is more powerful, effective, straightforward, and fruitfulness to study analytically other nonlinear complex physical models in plasma physics, mathematical physics, fluid mechanics, hydrodynamics, mathematical biology and many other physical sciences.

Construction of bright–dark solitons and ion-acoustic solitary wave solutions of dynamical system of nonlinear wave propagation

The nonlinear (2 + 1)-dimensional Zakharov–Kuznetsov (ZK) equations deal with the nonlinear behavior of waves in collision-less plasma, which contains non-isothermal cold ions and electrons. Two-dimensional dust acoustic solitary waves (DASWs) in magnetized plasma, which consist of trapped electrons and ions are leading to (2 + 1)-dim (ZK) equation by using the perturbation technique. We found the solitary wave solutions of (2 + 1)-dimensional (ZK)-equation, generalized (ZK)-equation and generalized form of modified (ZK)-equation by implementing the modified mathematical method. As a result, we obtained the bright–dark solitons, traveling wave and solitary wave solutions. The physical structure of obtained solutions is represented in 2D and 3D, graphically with the help of Mathematica.

Analytical solitary wave solution of the dust ion acoustic waves for the damped forced modified Korteweg-de Vries equation in q-nonextensive plasmas

Analytical solitary wave solution of the dust ion acoustic waves is studied due to the damped forced modified Korteweg-de Vries equation in an unmagnetized collisional dusty plasma consisting of negatively charged dust grain, positively charged ions, q-nonextensive electrons, and neutral particles in the presence of external periodic force. Using reductive perturbation technique, the damped forced modified Korteweg-de Vries equation is obtained for the dust ion acoustic waves. Momentum consevation law is used to obtain the dust ion acoustic solitary wave solutions in the framework of the damped forced modified Korteweg-de Vries equation. The effects of different physical parameters such as entropic index, dust ion collisional frequency, strength and frequency of the external periodic force, speed of the traveling wave and the parameter which is the ratio between the unperturbed densities of the dust ions and electrons are investigated on the analytical solution of the dust ion acoustic waves. It is observed that those parameters have significant effects on the structures of the damped forced dust ion acoustic solitary waves. The results of the present paper may have applications in laboratory and space plasma environments.

Propagation of kink and anti-kink wave solitons for the nonlinear damped modified Korteweg–de Vries equation arising in ion-acoustic wave in an unmagnetized collisional dusty plasma

In this research work, we investigate the dust ion-acoustic solitary wave in an unmagnetized collisional dusty plasma, which consists on ions having positive charge, dust fluid with negative charge, q nonextensive electrons and background neutral particles. We formulated nonlinear model by the damped modified Korteweg–de Vries (D-mKdV) equation by applying reductive perturbation technique. We also constructed the new solitary wave solutions for nonlinear D-mKdV equation with the help of two techniques. The obtained solutions are new and general and having the structure in the form of solitons, kink and antikink wave solitons, traveling waves, periodic solitary wave and we also show the structure of obtained solutions by two-dim and three-dim graphical by using the Mathematica to know the physical interpretation of different structure of DIASWs. These obtained solutions are more useful in the development of quantum plasma, dynamics of solitons, dynamics of fluid, problems of biomedical, dynamics of adiabatic parameters, industrial phenomena and many other branches. The calculations show that these techniques are more effective, fruitfulness and powerful to investigate analytical other nonlinear physical models of PDEs involves in Mathematical physics, plasma physics, Geo physics, fluid mechanics, hydrodynamics, mathematical biology, field of engineering and many other physical sciences.

Dust Ion Acoustic Solitary Waves in Multi-Ion Dusty Plasma System

A theoretical work has done to observe the existence of dust ion-acoustic (DIA) solitary waves (SWs) in a multi-ion dusty plasma system consisting of inertial positive and negative ions, Maxwell’s electrons, and arbitrary charged stationary dust. In this short communication, our research declares that with these components the derivation of Korteweg-de Vries (K-dV) and mixed K-dV (mK-dV) is possible. Here reductive perturbation method has been employed in all these approaches. The first K-dV equation has been derived which gave both bright and dark solitons but for a very limited region. Then the mK-dV equation has been derived that gave bright soliton for a large region, but no dark soliton has been observed.

Stability of three-dimensional dust acoustic waves in a strongly coupled dusty plasma including kappa distributed superthermal ions and electrons

A rigorous theoretical investigation of multi-dimensional instability of dust acoustic (DA) solitary waves in strongly coupled dusty plasma (SCDP) composed of superthermal distributed ions and electrons is presented. The dynamics of linear and nonlinear electrostatic excitations are studied. The dispersion properties of linear DA solitary waves are discussed in details. A nonlinear Zakharov-Kuznetsov (ZK) equation adequate for describing DA solitary waves is also derived. At the vicinity of the critical phase velocity, an extended ZK (EZK) equation is derived. The effects of the electrons and ions superthermality, the strongly and weakly coupling cases, and the ion-to-electron temperature ratio are discussed. The growth rate of the produced waves is calculated. It is found that the DA phase velocity decreases as the ion-to-electron temperature ratio increases. The contrary is occurred for strongly coupled system. The instability growth rate increases (decreases) by increasing the ion-to-electron temperature ratio (the superthermal parameters). The present investigation could be helpful in understanding the propagation and the instability of the detected DA solitary waves in laboratory, space and astrophysics mediums where superthermal particles are present.

Effects of Vortex-Like Ion Distribution on Dust-Acoustic Solitary Waves in a Self-Gravitating Opposite Polarity Dusty Plasmas

A self-gravitating opposite polarity dust plasma (SGOPDP) medium (containing both positively and negatively charged dust, vortex-like distributed ions and Maxwellian electrons) has been considered in order to examine the effect of vortex-like (trapped) ion distribution on dust-acoustic (DA) solitary waves (SWs) propagating in SGOPDP medium. The reductive perturbation method, which is valid for small but finite amplitude SWs, is employed to derive a modified Korteweg-de Vries equation having stronger nonlinearity. The basic features of the DA SWs in SGOPDP medium are found to be significantly modified by the combined effect of self-gravitational field and vortex-like ion distribution. The results of this paper have many implications in space and laboratory dusty plasmas.

Propagation of dust ion acoustic solitary waves in dusty plasma with Boltzmann electrons

In this multispecies plasma model, consisting of negative mobile dusts, non-thermal ions and Boltzmann electrons, dust-ion acoustic solitary waves are studied through reductive perturbative technique by deriving corresponding Korteweg-de Vries (KdV) equation. The number of dust charge contained in a dust particle (Zd) and the streaming speeds of mobile dusts (ud0) and ions (ui0) are observed to play very important role to form dust-ion acoustic compressive and rarefactive KdV solitons. Remarkably, some initial streaming of dust (ud0) are found to be instrumental for both compressive and rarefactive KdV solitons in a short range of Zd separating both kinds by some asymptotic lines. Also, the presence of low dust charges and lower ion streaming, compressive and rarefactive KdV solitons of either concave or convex characters are shown to reflect. For the higher streaming of mobile dusts, the amplitudes of the rarefactive KdV solitons characteristically changes from higher to lower showing convex character for this plasma model. A rigorous theoretical investigation has been made to show how the number of dust charge contained in a dust particle (Zd) drastically change the amplitudes of the compressive and rarefactive KdV solitons.

Evolution of dust ion acoustic soliton in the presence of superthermal electrons

Propagation of solitary wave in dusty plasmas started to draw the attention of the physicists since the early 90s. The presence of superthermal particles seems to have a great impact on such waves, as they indicate the existence of non-thermal systems. It has been observed that the superthermal population is capable of altering the nature of the plasmas waves. In the present paper, the effect of the superthermal electron population on the dust ion acoustic solitary wave has been explored. The plasma is considered un-magnetized and composed of two components of superthermal electrons (of two distinct temperature) along with positive ions, and negative dust particles. A major part of the work has been concentrated on the stability of the solitary structures considering the effect of the superthermal parameter. In addition, the dust charge has been considered as a variable and a detailed analysis has been provided on the same. The proposed plasma model is most suitable for analyzing Saturn magnetosphere and can be extended to any space plasmas with superthermal population.

Nonlinear dust acoustic waves in a self-gravitating and opposite-polarity complex plasma medium

The effects of the self-gravitational and the polarization forces on dust acoustic waves structure in a two-fluid complex plasma model are studied. The electrons and the ions obey the non-extensive distribution. The nonlinear dynamics of the massive positive and negative dust grains are considered. The reductive perturbation technique is applied to obtain a Zakharov-Kuznetsov equation. The nonlinear characteristics of the dust acoustic cnoidal (periodic) and solitary waves are investigated using the bifurcation theory. It is found that the dust acoustic wave properties depend strongly on the gravitational and the polarization parameters as well as the non-extensive indexes for electrons and ions. The possible applications of the present work to space plasma situations are discussed.

Dust Acoustic Solitary Waves in a Five Component Plasma-Application to Comets

We have studied the characteristics of the Dust Acoustic Solitary Wave (DASW) in a five component cometary plasma composed of two components of electrons (one hotter and one colder), hydrogen ions and a pair of oppositely charged dust particles (heavier ions). The Korteweg – deVries wave equation has been derived for the system and its solitary wave solution obtained. The dust acoustic solitary wave amplitude is almost a constant with varying temperatures of the hot electron component but decreases with increasing hydrogen ion densities. A comparison with a complementary nonlinear wave, the Dust Ion Acoustic Solitary Wave, has also been made. Keywords: Dust acoustic solitary wave, K dV equation, kappa distributed ions and electrons Cite this Article Neethu Theresa Willington, Sijo Sebastian, Chandu Venugopal. Dust Acoustic Solitary Waves in a Five Component Plasma-Application to Comets. Research & Reviews: Journal of Physics . 2019; 8(2): 44–51p.

Cylindrical and Spherical Dust-Ion Acoustic Solitary Waves by Damped Korteweg-de Vries-Burgers Equation

Theoretical investigations are carried out for the cylindrical and spherical dust-ion acoustic solitary waves with the kinematic viscosity. By the reductive perturbation technique the damped KdV-Burgers equation is obtained, and an approximate analytical solution is given. Using this solution, the effects of different physical parameters on dust-ion acoustic solitary wave are discussed. The results may have applications in laboratory and space plasmas.

KdV acoustic structure with exchange-correlation potential in plasmas

The effect of the exchange-correlation potential (ECP) on the profile of dust-acoustic solitary waves (DASWs) in dusty plasma containing degenerate electrons and ions was investigated. The present study focuses on the linear and nonlinear long-wavelength dust-acoustic waves in non-relativistic plasmas. The linear acoustic waves are analyzed using the multi-fluid model, whereas the reductive perturbation theory is applied to derive a modified Korteweg-de Vries (KdV) equation for small- but finite-amplitude waves. The effects of dust concentration and the exchange-correlation potential were investigated. These parameters remarkably change the amplitude and the width of the solitary waves. The findings from this investigation may lead to further understanding of the characteristics of nonlinear electrostatic waves exciting in the dense Fermi gas which is present in metallic nano structures or in near-supernovae environment in the presence of massive charge defects.

Formation of highly nonlinear dust-acoustic solitary waves due to high-temperature electrons and ions

The nonlinear propagation of dust-acoustic solitary waves (DASWs) in an unmagnetized dusty plasma consisting of two distinct temperature ions, two distinct temperature electrons and mobile dust fluid has been investigated by employing reductive perturbation method. It has been assumed that the two distinct temperature ions follow the Maxwell–Boltzmann distribution and nonthermal (Cairn’s) distribution separately while the two distinct temperature electrons follow the nonextensive (Tsallis) distribution and superthermal (Kappa) distribution separately. The system has been treated by deriving and solving a set of three highly nonlinear equations such as K-dV, modified K-dV and Gardner equations. It has been noted that the basic properties of the DASWs are significantly modified by the presence of the nonthermal ions, nonextensive electrons and superthermal electrons. The possible applications of this investigation in astrophysical, space and laboratory plasma systems have also been briefly addressed.

Effect of variable dust size, charge and mass on dust acoustic solitary waves in nonextensive magnetized plasma

Effects of variable dust size, mass and charge on the characteristics of nonlinear dust acoustic solitary waves (DASW) in a two-temperature ion dusty plasma have been studied analytically. Plasma ions are assumed to be Maxwellian while plasma electrons are nonextensively distributed. Mass and electrical charge of dust particles are assumed to be proportional to their size. Plasma is embedded in an external magnetic field with variable direction. The Zakharov–Kuznetsov equation was derived using reductive perturbation method, and its solitary answers were extracted. Dispersion relation of DASW shows that this wave may generate in plasma only if the nonextensivity coefficient, q, is positive. For all allowed magnitudes of c (the ratio of the largest dust radius to smallest dust radius) and q, only rarefactive solitons may be formed in plasma. Effect of variable dust size on the width and amplitude of DASW is noticeable when c is smaller than 3. Both the width and amplitude of DASW increase with increasing c, and with increasing the nonextensivity of plasma, effect of variable size increases. Results show that increasing the strength of external magnetic field leads to localization of DASW while both the width and amplitude of DASW are under the influence of the direction of the external magnetic field simultaneously.

Influence of dust-neutral collisional frequency and nonextensivity on dynamic motion of dust-acoustic waves

ABSTRACT Influence of dust-neutral collisional frequency and nonextensivity on the linear and nonlinear dust-acoustic waves is studied in a magnetized collisional dusty plasma, which consists of negatively charged cold dust particles, q-nonextensive hot ions and hot electrons with stationary neutrals considering the dust-neutral collisions. It is observed through linear mode analysis that linear dust-acoustic wave behaves like a damping wave and its damping rate mainly depends on dust-neutral collisional frequency (). The damped Zakharov and Kuznetsov (ZK) equation is obtained employing the reductive perturbation technique. The effects of dust-neutral collisional frequency () and nonextensive parameter (q) are observed on the characteristic features of dust-acoustic solitary waves. Control of dynamic motions for dust-acoustic waves is investigated considering three-dimensional phase portraits, time-series analysis and sensitivity analysis. The parameters , and play vital roles on the control of dynamic motions for dust-acoustic waves in presence of the external periodic force. Our study may be helpful to understand the behavior of dust-acoustic wave in the magnetosphere.

Analytical solutions of cylindrical and spherical dust ion-acoustic solitary waves

Abstract In the present work, employing the conventional reductive perturbation method to the field equations of an unmagnetized dusty plasma consisting of inertial ions, Boltzmann electrons and stationary dust particles in the nonplanar geometry we derived cylindrical(spherical) KdV and mKdV equations. Being aware of the fact that there exists no exact analytical solution for the progressive waves for such evolution equations we presented the exact analytical solution of a generalized form of such evolution equations in the planar geometry and used this solution to obtain an analytical approximate progressive wave solution to the generalized evolution equation. Then the progressive wave solutions for the cylindrical(spherical) KdV and m-KdV equations is obtained as some special cases. The analytical approximate solutions so obtained are compared with the numerical solutions of these equations. The results reveal that both solutions are in a good agreement. One advantage of present analytical approximate solution is that it allows readers to gain information, share understandings, or carry out a physical parametric study on the evolution solution behavior as well as the solution calculation has no CPU time-consuming or round off error.