Rarefactive Solitons Research Articles

Head-on collision of ion-acoustic solitons in collisional pair ions plasmas with non-Maxwellian electrons

The head-on collisional phenomena concerning ion acoustic waves are investigated considering collisional plasma system comprises of pair ions and hybrid non-Maxwellian electrons. The two-sided Korteweg–de Vries (KdV) equations are derived using extended poincaré-Lighthill-Kuo (ePLK) method. The effects of superthermal index () related to kappa distributed electrons, nonthermal parameter () related to the Cairn’s distributed electrons, density ratio of electron to positive ion (), and temperature ratio () of positive to negative ion on the phase velocity, spatiotemporal evolutions of amplitude, width, time dependent phase shifts and velocity of the right propagating solitons as well as the production of KdV solitons are investigated. Both the rarefactive and compressive soliton structures are produced due to head-on collision depending on plasma parameters. It is found that phase velocity is increasing (decreasing) due to the enhancement of and (). The amplitude of right traveling soliton increases (decreases) with increasing (), while and show opposite characteristic behaviors due to the plasma parameters concerned.

Nonlinear drift ion acoustic waves in degenerate plasmas with adiabatic trapping

In this work, we have investigated ion acoustic drift waves in the presence of adiabatically trapped degenerate electrons in both linear and nonlinear regimes. Using quantum magnetohydrodynamics (QMHD), we have modelled a new nonlinear wave equation with a fractional nonlinearity in two spatial dimensions and one temporal coordinate. We have carried out the nonlinear analysis by using Sagdeev potential approach and obtained arbitrary amplitude rarefactive solitons. The propagation ranges for these solitons are worked out with regard to inhomogeneity and obliqueness. For illustrative purposes, we have applied our results to neutron stars [5] where the quantum effects are surmised to be extremely significant.

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.

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.

Interaction phenomena and effect of higher order dispersion on electron acoustic solitary waves in weakly relativistic regimes

AbstractThe interaction phenomena of electron acoustic solitary waves (EASWs) and the higher order correction of Korteweg‐de Vries (KdV) equations (KdVEs) have investigated in unmagnetized collisionless plasma system consisting of relativistic cold electrons and electron beams, non‐relativistic Maxwellian hot electrons and stationary ions. To understand the physical issues concerned, the two‐sided KdVEs using extended Poincaré‐Lighthill‐Kue (ePLK) method are derived taking the higher order correction into consideration. The analyses reveal that the widths and amplitudes of EASWs (as obtain from KdVEs) are decreasing with plasma parameters. The plasma parameters are responsible for the modification of KdV‐soliton structure. It is found that the narrowness of width and the steepness of dip of the solitons become more pronounced and the electric field behaves like semi‐kink solitons due to the higher order correction of KdVEs. Dip shape rarefactive soliton becomes pronounced by plasma parameters. The phase shifts of EASWs are also enhanced due to the effects of plasma species temperatures and density ratios.

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.

Gravitoelectrostatic excitations in an opposite polarity complex plasma

The linear and nonlinear properties of gravitoelectrostatic mode, in a plasma system consisting of inertial opposite polarity charged dust grains as well as inertialess nonextensively q-distributed ions and electrons (including the effect of polarization force on the massively charged dust grains), have been investigated. A general dispersion relation has been derived yielding only one eigen wave mode. It is found that the polarization force and the nonextensively distributed ions effects play directly a destabilizing role in Jeans instability. Moreover, a new pair of gravitoelectrostatically coupled energy integral equation has been obtained by applying the Sagdeev pseudopotential technique. Also, a small-amplitude approximation is considered for the self-gravitational potential. It is reported that the fluctuations dynamics of the dust grains evolve self-gravitational rarefactive soliton pulses and electrostatic compressive soliton-like patterns. Applying the phase plane analysis, the phase portraits of the dynamical system have been presented and also the corresponding wave solutions. Our results could be applicable for different space and astrophysical plasma systems, particularly for dust molecular clouds of H-II region.

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.

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.

Solitary dispersive Alfvén wave in a plasma composed of hot positrons, cold electrons and ions

The nonlinear solitary structure of the dispersive Alfvén wave in an three-component plasma with hot positron, cold electron and ion is studied from the multi-fluid theory. It is found that when the equilibrium number density ratio of ion to electron is finite, there only exists the super-Alfvén rarefactive solitons. The increase of the ion concentration or the speed of soliton will lead a deeper depletion of the electron number density. The width of soliton decreases with the increase of the speed of soliton and the ion concentration. When the equilibrium number density ratio of ion to electron is much less than unity, there are only sub-Alfvén rarefactive solitons. In the case, the larger speed of soliton or the smaller concentration of ions result the deeper depletion of the electron number density. The width of the soliton increases with the ion concentration and the speed of soliton. The results obtained may be related to the observations and experimental results in the electron positron plasma.

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.

Electrostatic cnoidal waves and soliton structures in multi‐ions plasmas

Using a reductive perturbation technique (RPT), the Korteweg‐de Vries (KdV) equation for nonlinear electrostatic waves in multi‐ion plasmas is derived with appropriate boundary conditions. Furthermore, compressive and rarefactive cnoidal wave and soliton solutions are discussed. In our model, the multi‐ion plasma consists of light dynamic warm ions, heavy cold ions, and inertialess electrons, which follows the Maxwell‐Boltzmann distribution. It is observed that in such an unmagnetized multi‐ion plasma, two characteristic electrostatic waves i.e., slow ion‐acoustic (SIA) waves and fast ion‐acoustic (FIA) waves, can propagate. The results are discussed by considering two types of multi‐ion plasmas i.e., H+–O+–e plasma and H−–O+–e plasma that exist in space plasmas. It is found that for H+–O+–e plasma, the SIA cnoidal wave and soliton form both positive (compressive) and negative (rarefactive) potential pulses, which depend on the temperature and density of the light and warm ions. However, only electrostatic positive potential structures are obtained for FIA cnoidal wave and soliton in H+–O+–e plasma. In the case of H−–O+–e plasma, the SIA cnoidal wave and soliton form only compressive structures, while the FIA cnoidal wave and soliton compose rarefactive structures. The effects of light ions' density and temperature on nonlinear potential structures are investigated in detail. The parametric results are also demonstrated, which are applicable to space and laboratory multi‐ion plasma situations.

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.