Compressive Solitons Research Articles

On a semiclassical model for damped dust ion-acoustic solitons with analysis of quantum electron exchange-correlation potential

The semiclassical hydrodynamic model is used to study the effect of electron exchange-correlation potential, quantum Bohm term, and degenerate pressure on the dynamics of dust ion acoustic waves by following the two-fluid theory in collisional, unmagnetized dusty plasma. For linear analysis, the dispersion relation modified by the exchange-correlation coefficient is derived. For nonlinear analysis, the standard perturbative approach is used to derive a deformed Korteweg–deVries equation with a linear damping term for finite amplitude waves. The analytical and numerical investigations in the presence of low collisional frequencies reveal the existence of compressive dissipative solitons. Considering the dense astrophysical objects, the dissipative compressive solitons are numerically investigated with the effect of different plasma parameters including collisions and exchange-correlation potential.

Ion-acoustic gardner solitons and double layers in magnetized electron-positron-ion quantum plasma

The nonlinear propagation of ion-acoustic Gardner solitons (GSs) and double layers (DLs) in electron-positron-ion (EPI) plasma in the presence of an external static magnetic field has been examined. The Korteweg–de Vries (KdV), modified KdV (mKdV), and Gardner equations have been derived by the reductive perturbation technique. It is seen that the amplitude, polarity, speed, width of such solitons are significantly modified by the species densities and by the obliquity angle. Compressive or rarefactive KdV solitons are obtained, but only compressive solitons are obtained in the mKdV case, wherever Gardner positive and negative DLs exist. The results of our present investigation may be useful for understanding the nonlinear wave propagation in dense quantum plasmas such as those existing in white dwarfs, neutron stars and intense laser-solid matter interaction experiments as an example of laboratory plasmas.

On the Characteristics of Solitary Waves and Shocks in Nonextensive Plasmas: Collisionality and Kinematic Viscosity Effects

In this article, a comprehensive investigation of the linear and nonlinear waves’ structure in an unmagnetized plasma consisting of nonextensive electrons, considering collisionality and kinematic viscosity effects, is studied. Using a reductive perturbation technique, we have derived a hybrid Korteweg–de Vries–Burgers equation for ion-acoustic (IA) waves. Analytical solutions for solitary waves and shock structures are obtained. We have also solved this equation numerically in order to investigate the basic properties of solitary/shock waves in such a plasma system. The presence of nonextensive electrons with $q$ -distribution influences significantly the solitary and shock wave structures. In other words, the compressive and rarefactive-type solitons or shock waves can also be seen in this plasma model depending on the strength of nonextensivity. On the other hand, the effects of ion-neutral collision and ion kinematic viscosity on the characteristics of IA solitary/shock waves are discussed. It is found that these parameters modify the basic features of the solitonic and shock excitations.

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.

Dust acoustic solitons in an opposite polarity dusty plasma in the presence of generalized polarization force

Propagation characteristics of dust acoustic (DA) solitons in an opposite polarity dusty plasma medium containing inertial positive and negative dust grains and inertialess ions and electrons following Maxwellian distribution have been theoretically investigated by taking the effect of generalized polarization force into consideration. By using the reductive perturbation method, the Korteweg–de Vries equation that governs the nonlinear dust acoustic waves has been derived. It has been found that rarefactive and compressive solitons (solitons associated with negative and positive potentials) propagate in such a dusty plasma medium. The dependence of soliton characteristics on the system parameters has been discussed. It is observed that the basic properties of the DA solitons are significantly modified by the effects of generalized polarization force, ion-to-electron temperature ratio, and positive dust component. The findings of this investigation may be used in understanding the wave propagation in space and laboratory plasmas in which dust of opposite polarity coexists under the polarization force.

Obliquely propagating quantum solitary waves in quantum‐magnetized plasma with ultra‐relativistic degenerate electrons and positrons

AbstractThe oblique propagation of the quantum electrostatic solitary waves in magnetized relativistic quantum plasma is investigated using the quantum hydrodynamic equations. The plasma consists of dynamic relativistic degenerate electrons and positrons and a weakly relativistic ion beam. The Zakharov‐Kuznetsov equation is derived using the standard reductive perturbation technique that admits an obliquely propagating soliton solution. It is found that two types of quantum acoustic modes, that is, a slow acoustic mode and fast acoustic mode, could be propagated in our plasma model. The parameter that determines the nature of soliton, that is, compressive or rarefactive soliton, for slow mode is investigated. Our numerical results show that for the slow mode, the determining parameter is ion beam velocity in the case of relativistic degenerate electrons. We also have examined the effects of plasma parameters (like the beam velocity, the density ratio of positron to electron, the relativistic factor, and the propagation angle) on the characteristics of solitary waves.

The Role of Modified Boltzmann Relation With Electron Inertia on the Evolution of Solitary Waves Derived by Energy Integral Method Along With the Comparative Studies on Soliton Dynamics in Generalized Multi-Component Plasma

The nonlinear solitary waves in multi-component plasmas coexisting with negative ions, relativistic, and nonrelativistic electrons have been investigated under the influence of a modified Boltzmann relation with electron inertia $m_{\text {e}}$ (mass of electrons $\ne 0$ ) by Sagdeev potential and perturbation methods. The supersonic and subsonic compressive solitons are shown to be dependable on higher negative ion concentrations and the direction of wave propagation ( $k_{x} $ ). The condition of characteristic representation of the new Boltzmann relation appears to generate substantially high amplitude rarefactive solitons based on the direction of propagation, negative to positive ion mass ratio $r$ (>1), and high Mach number $M$ . The relativistic effects in non-Boltzmann electrons causing an increase in mass are responsible for the change in the growth of solitons in plasma.

Interaction phenomena of ion acoustic solitary waves with singly charged cold ions and Boltzmann electrons

The linear features and phenomena concerning head-on collision between the two ion acoustic solitary waves are investigated considering the multi-component plasma system comprising singly charged cold positive and negative ions, and Boltzmann electrons. Linear characteristics of ion acoustic solitary waves are studied taking the dispersion relation into account. The two-sided Korteweg-de Vries (KdV) equations are derived to investigate the structures of the solitons and the phase shift of ion acoustic solitary waves due to collisions by the extended Poincaré-Lighthill-Kuo (ePLK) method. The linear analyses reveal that the densities of the ionic species and wave number modify the ion acoustic solitary wave frequency, and higher density of electrons changes the group velocity. It is found that a new wave is produced with high amplitude in the interaction region due to head-on collision between the waves. The compressive and rarefactive KdV solitons are produced due to the changes of density. The density ratios such as and modify the phase shift and nonlinear phase velocity after head-on collision.

Propagation of dust ion acoustic wave in a uniform weak magnetic field

The effects of the obliqueness and the strength of the external magnetic field on the propagation ion acoustic wave in a dusty plasma are investigated. The dispersion relation of the electrostatic wave is found to be modified by the Lorentz force. The reductive perturbation technique is used to derive the equation of propagation of the electrostatic potential of the wave, known as the rotation-modified Korteweg-de Vries (rmKdV) equation. The time evolution of the electrostatic solitary wave, propagating obliquely to the background magnetic field, is numerically studied for different values of the right-hand side of the (rmKdV) equation. It is found that for small values of the right-hand side of the (rmKdV) equation, both compressive and rarefactive solitons undergo a decay by radiating energy to the tails, who themselves steepens to produce a secondary solitary wave who will in turn suffer another decay. This Scenario of decay and steepening is repeated indefinitely. However, for the high value of the right-hand side of the (rmKdV) equation, the soliton is unstable as it propagates and non-stationary waves must be formed.

Nonlinear Dispersive and Dissipative Electrostatic Structures in Two-Dimensional Electron-Positron-Ion Quantum Plasma

The nonlinear features of two-dimensional ion acoustic (IA) solitary and shock structures in a dissipative electron-positron-ion (EPI) quantum plasma are investigated. The dissipation in the system is taken into account by incorporating the kinematic viscosity of ions in plasmas. A quantum hydrodynamic (QHD) model is used to describe the quantum plasma system. The propagation of small but finite amplitude solitons and shocks is governed by the Kadomtsev-Petviashvili-Burger (KPB) equation. It is observed that depending on the values of plasma parameters (viz. quantum diffraction, positron concentration, viscosity), both compressive and rarefactive solitons and shocks are found to exist. Furthermore, the energy of the soliton is computed and possible solutions of the KPB equation are presented numerically in terms of the monotonic and oscillatory shock profiles

Collisions of acoustic solitons and their electric fields in plasmas at critical compositions

Acoustic solitons obtained through a reductive perturbation scheme are normally governed by a Korteweg–de Vries (KdV) equation. In multispecies plasmas at critical compositions the coefficient of the quadratic nonlinearity vanishes. Extending the analytic treatment then leads to a modified KdV (mKdV) equation, which is characterized by a cubic nonlinearity and is even in the electrostatic potential. The mKdV equation admits solitons having opposite electrostatic polarities, in contrast to KdV solitons which can only be of one polarity at a time. A Hirota formalism has been used to derive the two-soliton solution. That solution covers not only the interaction of same-polarity solitons but also the collision of compressive and rarefactive solitons. For the visualization of the solutions, the focus is on the details of the interaction region. A novel and detailed discussion is included of typical electric field signatures that are often observed in ionospheric and magnetospheric plasmas. It is argued that these signatures can be attributed to solitons and their interactions. As such, they have received little attention.

Dust Charging and Propagation of Dust-Acoustic Waves in a Multicomponent Thermal Dusty Plasma System

An analytical model is developed with the aim to investigate the propagation of dust-acoustic (DA) waves in a multicomponent thermal dusty plasma system including ion species as well. Dust particles are considered positively charged by electron and ion currents, thermionic and UV photo-ionic processes. The model is applied to laboratory plasma as well as Martian atmospheric plasma to explain the nature of dust potential variation as well as characteristics of DA propagation modes within the linear and nonlinear regimes for given plasma parameters. In the nonlinear regime, the KdV equation is derived, and the equation is seen to support the propagation of compressive solitons in laboratory plasma system and rarefactive solitons in the case of Martian atmospheric plasma. The inclusion of ion species in the system is seen to have an important role in determining the propagation speed, the amplitude, and the corresponding width of solitons. The thermionic work function W, photon yield factor Y, and low value of flux density of UV photon beam J do not have an appreciable impact on dispersion relation and DA soliton structures. On the contrary, noticeable changes occur in the case of the dust surface potential obtained in both laboratory and Martian plasmas.

Magnetoacoustic solitons in pair-ion fullerene plasma

ABSTRACT The propagation of magnetoacoustic (fast magnetohydrodynamic) waves in pair-ion (PI) fullerene plasma is studied in the linear and nonlinear regimes. The pair-ion (PI) fullerene plasma is theorized as homogeneous, magnetized, warm and collisionless. Employing multi-fluid magnetohydrodynamic model, the dispersion relation is obtained and wave dispersion effects which appear through ion inertial length are discussed. Using reductive perturbation technique (RPT), the Korteweg–de Vries (KdV) equation is derived and its solution for small but finite amplitude magnetoacoustic solitons propagating in the direction perpendicular to the external magnetic field is presented. The compressive magnetoacoustic soliton (i.e. positive potential pulse) propagating with super Alfvénic speed is obtained in magnetized PI fullerene plasma. The variations in the amplitude and width of the magnetoacoustic soliton structures are also illustrated by using numerical values of the plasma parameters such as ions' density, temperature difference between fullerene ions and magnetic field intensity, which have been taken from the PI plasma experiments already published in the literature.

Interaction of magnetoacoustic solitons in electron-positron plasmas

The interaction between two, four and six magnetoacoustic solitons in electron-positron plasmas are investigated. The extended Poincaré–Lighthill–Kuo (PLK) perturbation method is employed to derived two KdV equations for magnetoacoustic solitons moving towards each other and studied the head-on collision between them and their phase shifts. The Hirota bilinear method is used to have multi-soliton solutions of already derived two KdV equations for right and left moving solitons. The four and six magnetoacoustic solitons solutions of the two KdV equations are obtained to discuss their interaction and phase shifts. It is found that only compressive magnetoacoustic solitons structures are formed in electron-positron plasma. The present study may be useful to understand the collective phenomena related to head-on and overtaking magnetoacoustic solitons interaction in electron-positron plasmas that may occur in a pulsar magnetosphere.

Ion-acoustic Gardner solitons in multi-ion degenerate plasma with the effect of polarization and trapping in the presence of a quantizing magnetic field

A theoretical investigation is presented for ion-acoustic Gardner solitons (GSs) and double layers (DLs) in a multi-ion plasma system. The plasma consists of inertial positively and negatively charged ions and negatively charged immobile heavy ions and electrons which are in trapping distribution, all existing in a quantizing magnetic field. The reductive perturbation method is used to derive Korteweg-de Vries (KdV), modified KdV (mKdV), and Gardner equations. It is found that the KdV solitons and Gardner solitons (GSs) are either compressive or rarefactive depending on the plasma parameters, whereas only compressive solitons are obtained in the mKdV case, wherever Gardner positive DLs exist. These solitons are significantly modified due to the introduction of the trapping parameter and polarization coefficient. The presented results are considered to be beneficial in understanding the solitary structures in dense quantum plasmas such as those existing in white dwarfs.

Interaction of magnetoacoustic solitons in plasmas with dispersion effects through electron inertia

The head‐on collision between two magnetoacoustic solitons is investigated in a magnetized plasma containing inertial cold ions and warm electrons. A two‐fluid magnetohydrodynamic (MHD) model is used to study the magnetoacoustic solitons interaction in plasmas. The magnetoacoustic wave dispersion effects appearing through electron inertial length (skin depth) are also included in the model. By using the extended Poincaré–Lighthill–Kuo (PLK) method, the Korteweg–de Vries (KdV) equations are derived for the low amplitude left and right moving magnetoacoustic solitons, their trajectories, and corresponding phase shifts after their elastic collisions are obtained analytically and examined numerically as well. It is found that only positive polarity (compressive) soliton structures of magnetoacoustic waves are formed. The profiles of head‐on collision and the time evolution of two compressive interacting magnetoacoustic solitons are also presented for illustration. The effect of plasma beta, which depends on plasma density, electron temperature, and magnetic field intensity, on the phase shift of the interacting magnetoacoustic solitons is also examined.

Head-on collision between positron acoustic waves in homogeneous and inhomogeneous plasmas

The head-on collision between positron acoustic solitary waves (PASWs) as well as the production of rogue waves (RWs) in homogeneous and PASWs in inhomogeneous unmagnetized plasma systems are investigated deriving the nonlinear evolution equations. The plasmas are composed of immobile positive ions, mobile cold and hot positrons, and hot electrons, where the hot positrons and hot electrons are assumed to follow the Kappa distributions. The evolution equations are derived using the appropriate coordinate transformation and the reductive perturbation technique. The effects of concentrations, kappa parameters of hot electrons and positrons, and temperature ratios on the characteristics of PASWs and RWs are examined. It is found that the kappa parameters and temperature ratios significantly modify phase shifts after head-on collisions and RWs in homogeneous as well as PASWs in inhomogeneous plasmas. The amplitudes of the PASWs in inhomogeneous plasmas are diminished with increasing kappa parameters, concentration and temperature ratios. Further, the amplitudes of RWs are reduced with increasing charged particles concentration, while it enhances with increasing kappa- and temperature parameters. Besides, the compressive and rarefactive solitons are produced at critical densities from KdV equation for hot and cold positrons, while the compressive solitons are only produced from mKdV equation for both in homogeneous and inhomogeneous plasmas.

Weakly Relativistic Ion-Acoustic Solitary Waves in Dusty Plasma

The streaming speeds of relativistic electrons ( $v_{e0})$ and ions ( $v_{i0})$ together with the negative dust charge $Z_{d}$ of immobile dust particles are observed to play characteristic role in the formation of dust ion-acoustic (DIA) compressive and rarefactive relativistic solitons in this plasma model. The critical value of the electron streaming ( $v_{e0})_{\mathrm{ crit}}$ in the process of generating solitary waves in this relativistic dusty plasma is shown to lie in the vicinity of the point/points, where $v_{e0} \approx v_{i0}$ . Further, the existence of compressive (rarefactive) solitons of much higher amplitudes is reflected in the immediate left (right) of this critical value ( $v_{e0})_{\mathrm{ crit}}$ within a short span of interval. Otherwise, the interval of existence of high-amplitude DIA compressive and rarefactive relativistic solitons is found to coincide with the assigned parametric domain of ion’s initial streaming ( $v_{i0})$ within the vicinity of electron’s ( $v_{e0}$ ’s) critical values. Moreover, the existence of critical range of $v_{i0}$ in a much lower domain suggests that the role of the massive ions in the presence of dust particles in the plasma is found predominant. A definite existence interval of $v_{i0}$ can be predicted for the generation of only DIA compressive relativistic solitons corresponding to every negligible value of $v_{e0}$ and large $Z_{d}$ in this model of dusty plasma. The high impact from the massive increase of negative charges $Z_{d}$ causes the extinction of compressive solitons at some upper limit of $v_{io}$ to earmark the interval of existence corresponding to each $Z_{d}$ .

Effects of dust polarity and nonextensive electrons on the dust-ion acoustic solitons and double layers in earth atmosphere

Propagation of dustion acoustic solitary waves (DIASWs) and double layers is discussed in earth atmosphere, using the Sagdeev potential method. The best model for distribution function of electrons in earth atmosphere is found by fitting available data on different distribution functions. The nonextensive function with parameter q=0.58 provides the best fit on observations. Thus we analyze the propagation of localized waves in an unmagnetized plasma containing nonextensive electrons, inertial ions, and negatively/positively charged stationary dust. It is found that both compressive and rarefactive solitons as well as double layers exist depending on the sign (and the value) of dust polarity. Characters of propagated waves are described using the presented model.

Study of the Characteristics of Dust Acoustic Solitary Waves and Dust Acoustic Shock Waves in Electron Free Dusty Space Plasma

A theoretical investigation has been done for the study of dust acoustic solitary waves and dust acoustic shock waves propagating in an unmagnetized, collisionless Lorentzian dusty plasma considering adiabatic and non-adiabatic dust charge variation. Plasma under consideration is composed of inertialess Lorentzian positive and negative ions along with inertial positively charged dust grains. Such dust grains are charged by the flow of positive ion and negative ion current over the grain surface. Adiabatic grain charge variation shows the existence of compressive soliton whose amplitude decreases and width increases with increasing number of suprathermal particles. Non-adiabatic dust charge variation is concerned with the propagation of monotonic dust acoustic shock waves which do not loose monotonicity even when a number of suprathermal particles are very large.