Investigation of solitary waves in warm plasma for smaller order relativistic effects with variable pressures and inertia of electrons

In the two component relativistic plasmas subject to pressure variation of adiabatic electrons and isothermal ions, both compressive and rarefactive KdV solitons are established in a quite different physical plasma model. It is desirable to define c _s in a new way to substantiate the validity of the model under relativistic effects. The corresponding mathematical condition is also determined, which is a new report of this kind. It is also interesting to report that the relativistic rarefactive solitons cease to exist below some critical ion initial streaming speed v _i0 for a fixed temperature α and electron streaming speed v _e0. Besides, higher initial flux v _i0 of ions under constant temperature is observed to generate higher speed v _i at the passage of time which causes to increase (in relativistic sense) its mass diminishing thereby the growth of soliton amplitudes.     

Investigation of ion acoustic solitons (IAS) in a weakly relativistic magnetized plasma

Compressive solitons of low and high amplitudes are established in this weakly relativistic and magnetized plasma model. The assigned direction of soliton propagation to the direction of the magnetic field, supplemented by the corresponding ion initial streaming speed (v _iξ0) determines the lower limit of the initial electron streaming speed (v _eξ0) in its interval of existence to produce solitons for a given value of the speed of light c. Further, lower limit of c specified by the corresponding energy (or temperature) to yield relativistic compressive solitons is also predicated. Interestingly, the increased initial streaming speed of electrons is found to play less effective role in the steepening growth of amplitudes of compressive solitons due to mode one than those corresponding to the mode two.     

Planar Gardner solitons and double layers in dusty electronegative plasmas with kappa distributed electrons

A theoretical investigation has been made on the Dust ion-acoustic (DIA) Gardner solitons (GSs) and double layers (DLs) in electronegative plasma consisting of inertial positive and negative ions, super-thermal (kappa distributed) electrons, and negatively charged static dust. The standard reductive perturbation method is employed to derive the Korteweg-de Vries (K-dV), modified K-dV (mK-dV), and standard Gardner equations, which admits solitary waves (SWs) and DLs solutions. It have been found that GSs and DLs exist for α around its critical value α _c , where α _c is the value of α corresponding to the vanishing of the nonlinear coefficient of the K-dV equation. The parametric regimes for the existence of both the positive as well as negative SWs and negative DLs are obtained. The basic features of DIA SWs and DLs are analyzed and it has been found that the polarity, speed, height, thickness of such DIA SWs and DLs structures, are significantly modified due to the presence of two types of ions and spectral index (κ) of super-thermal electrons. It has also been found that the characteristics of DIA GSs and DLs, are different from that of the K-dV solitons and mK-dV solitons. The relevance of our results to different interstellar space plasma situations are discussed.     

Interacting holographic dark energy with variable deceleration parameter and accreting black holes in Bianchi type-V universe

Dust-ion-acoustic (DIA) waves in an unmagnetized dusty plasma system consisting of inertial ions, negatively charged immobile dust, and superthermal (kappa distributed) electrons with two distinct temperatures are investigated both numerically and analytically by deriving Korteweg–de Vries (K-dV), modified K-dV (mK-dV), and Gardner equations along with its double layers (DLs) solutions using the reductive perturbation technique. The basic features of the DIA Gardner solitons (GSs) as well as DLs are studied, and an analytical comparison among K-dV, mK-dV, and GSs are also observed. The parametric regimes for the existence of both the positive as well as negative SWs and negative DLs are obtained. It is observed that superthermal electrons with two distinct temperatures significantly affect on the basic properties of the DIA solitary waves and DLs; and depending on the parameter μ _c (the critical value of relative electron number density μ _e1), the DIA K-dV and Gardner solitons exhibit both compressive and rarefactive structures, whereas the mK-dV solitons support only compressive structures and DLs support only the rarefactive structures. The present investigation can be very effective for understanding and studying various astrophysical plasma environments (viz. Saturn magnetosphere, pulsar magnetosphere, etc.).     

Effects of two temperature electrons on Gardner solitons and double layers in a nonthermal dusty electronegative plasma

Gardner solitons (GSs) and double layers (DLs) of dust ion acoustic (DIA) waves in an electronegative plasma (composed of inertial positive and negative ions, Maxwellian cold electrons, non-thermal hot electrons, and negatively charged static dust) are studied. The reductive perturbation method is employed to derive the Korteweg-de Vries (K-dV), modified K-dV, and standard Gardner equations, which admits solitary wave and DLs solutions for σ around its critical value σ _c (where σ _c is the value of σ corresponding to the vanishing of the nonlinear coefficient of the K-dV equation). The parametric regimes for the existence of the GSs and DLs, are obtained. The basic features of DIA GSs and DLs (associated with negative structure only) are analyzed. It has been found that the characteristics of DIA GSs and DLs, are different from that of the K-dV solitons and mK-dV (mixed K-dV) solitons. The implications of our results to different space and laboratory plasma situations are discussed.     

Compressive and rarefactive dust-acoustic Gardner solitons beyond the K-dV limit with two-temperature ions dusty plasma

The Gardner equation is derived and numerically solved. This equation shows the existence of compressive and rarefactive dust-acoustic (DA) solitons with two-temperature ions beyond the K-dV (Korteweg–de Vries) limit. These may be referred to as DA Gardner solitons (DA-GSs). Here we deal with a dusty plasma, composed of negatively charged cold mobile dust fluids, inertialess Boltzmann electrons and ions with two distinctive temperatures. The basic features of the compressive and rarefactive DA solitons are identified. These solitons are found to exist beyond the K-dV limit, i.e. they exist for μ _i1～μ _c. Here μ _i1=n _i10/Z _d n _d0, Z _d is the number of electrons residing upon the dust grain surface, and n _i0 (n _d0) is the lower temperature ion (dust) number density at equilibrium. These DA-GSs are completely different from the K-dV solitons, because μ _c (the critical value) corresponds to vanishing of the nonlinear coefficient of the K-dV equation, and μ _i1～μ _c corresponds to K-dV solitons, with extremely large amplitude, for which the validity of the reductive perturbation method breaks down. It has been found that, depending on whether the parameter μ _i1 is less than or greater than the critical value, the DA-GSs exhibit compression for μ _i1>μ _c and rarefaction for μ _i1<μ _c. The basic features of double layers with arbitrary amplitude are also briefly discussed, employing the pseudo-potential approach. The present investigation might be relevant to the electrostatic solitary structures observed in various cosmic dust-laden plasmas, such as supernova shells, Saturn’s F-ring, the ionopause of Halley’s comet, etc.     

Large amplitude dust ion-acoustic solitary waves in a plasma in the presence of positrons

Properties of propagation of large amplitude dust ion-acoustic solitary waves and double layers are investigated in electron-positron-ion plasma with highly charged negative dust. Sagdeev pseudopotential method has been used to derive the energy balance equation. The expression for the critical Mach number (lower/upper limit) for the existence of solitary structures has also been derived. The Sagdeev pseudopotential is a function of numbers of physical parameters such as ion temperature (σ), positron density (δ _p ), dust density (δ _d ) and electron to positron temperature ratio (β). These parameters significantly influence the properties of the solitary structures and double layers. Further it is found that both polarity (compressive and rarefactive) solitons and negative potential double layers are observed.     

Weakly relativistic solitary waves in multicomponent plasmas with electron inertia

Existence of compressive relativistic solitons is established in an arbitrary ξ-direction, inclining at an angle to the direction of the weak magnetic field (ω _pi ≫ω _Bi ) in this plasma compound with ions, relativistic electrons and relativistic electron beams. It is observed that the absolute linear growth of amplitudes of compressive solitons is due to inactive role of the weak magnetic field and the initial streaming speeds of relativistic electrons, electron beams, and Q _b (ion mass to electron beam mass). Besides, the small initial streaming of electrons is found to be responsible to generate relatively high amplitude compressive solitons. The non-relativistic ions in the background plasma, but in absence of electron-beam drift and in presence of weak magnetic field are the causing effect of interest for the smooth growth of soliton amplitudes in this model of plasma.     

Gardner solitons in dusty plasmas with nonextensive ions and two-temperature superthermal electrons

Nonlinear propagation of dust-acoustic waves in an unmagnetized dusty plasma consisting of negatively charged mobile dust, nonextensive ions following nonextensive q-distribution and two distinct temperature superthermal electrons following superthermal kappa distribution each, is investigated by employing lower and higher order nonlinear equations, namely the Korteweg-de-Vries (K-dV), the modified Korteweg-de-Vries (mK-dV) and the Gardner equations. The characteristic features of the hump (positive potential) and dip (negative potential) shaped dust-acoustic (DA) Gardner solitons are found to exist beyond the K-dV limit. The effects of two superthermal temperature electrons and ions nonextensivity on the basic characteristics of DA K-dV, mK-dV and Gardner solitons have also been investigated. It has been found that the DA Gardner solitons exhibit either negative or positive potential solitons only for q<q _c where, q _c is the critical value of the nonextensive parameter q. The possible applications of our results in understanding the localized nonlinear electrostatic structures existing in solar atmosphere, Saturn’s magnetosphere etc. (where the tails of the high energetic particles at different temperatures follow power-law like distribution) are also briefly discussed.     

Large amplitude acoustic solitons in a warm electronegative dusty plasma with q-nonextensive distributed electrons

Linear and nonlinear analysis are presented for an electronegative dusty plasma system. Linear analysis shows that the dispersive nature of the plasma system changes considerably due to the presence of nonthermal q-nonextensive distributed electrons. The presence of both compressive and rarefactive Sagdeev solitons is investigated and shown that the addition of even a small population of dust particles will significantly modify the large amplitude Sagdeev solitons. The coexistence of both compressive and rarefactive solitons for a certain set of parameters is also noticed in such system. The effect of variation of entropic index q, θ _i (ratio of positive ion temperature to electron temperature), θ _n (ratio of negative ion temperature to electron temperature) and dust particles concentration (R) is elaborated with the help of suitable parameters.     

Modified Jeans instability of magnetized viscous spin 1/2 quantum plasma with resistive effects and Hall current

Properties of ion acoustic solitons head-on collision in an ultracold neutral plasma composed of ion fluid and non-Maxwellian electron distributions are investigated. For this purpose, the extended Poincare-Lighthill-Kuo (PLK) method is employed to derive coupled Kortweg-de Vries (KdV) equations describing the system. The nonlinear evolution equations for the colliding solitons and corresponding phase shifts are investigated both analytically and numerically. It is found that the polarity of the colliding solitons strongly depends on the type of the non-Maxwellian distribution (via nonthermal or superthermal electron distributions). Especially the phase shift due to solitons collision is strongly influenced by the non-Maxwellian distribution. A new critical nonthermal parameter β _c , characterizing the nonthermal electron distribution, and which is not present for superthermal particle distributions, allows the existence of double polarity of the solitons. The phase shift increases below β _c for compressive solitons, but it decreases above β _c for rarefactive soliton. For superthermal distribution the phase shift increases rapidly for low spectral index κ, whereas for higher values of κ, the phase shift decreases smoothly and becomes nearly stable for κ>10. Around β _c and small values of κ, the deviation from the Maxwellian state is strongest, and therefore the phase shift has unexpected behavior due to the presence of more energetic electrons that are represented by the non-Maxwellian distributions. The nonlinear structure, as reported here, could be useful for controlling the solitons that may be created in future ultracold neutral plasma experiments.     

Ion acoustic solitons and double layers in electron–positron–ion plasmas with dust particulates

Propagation of small but finite amplitude ion acoustic solitons and double layers are investigated in electron–positron–ion plasmas in presence of highly negatively charged impurities or dust. The presence of negatively charged dust particulates can result in existence of two critical concentrations of ion–electron density ratio α. One of them α _D decides the existence of double layers, whereas the other one α _R decides the nature of the solitons and double layers. The system supports both compressive and rarefactive solitons as well as double layers. The parameter regimes of transitions from compressive to rarefactive solitons and double layers are also specified.     

Higher order corrections to dust-acoustic ZK-solitons in a magnetized quantum dusty plasma

Nonlinear propagation of two dimensional dust-acoustic solitary waves in a magnetized quantum dusty plasma whose constituents are electrons, ions, and negatively charged heavy dust particles are investigated using quantum hydrodynamic model. The Zakharov-Kuznetsov (ZK) equation is derived by using reductive perturbation technique (RPT). The higher order inhomogeneous ZK-type differential equation is obtained for the correction to ZK- soliton. The dynamical equation for dressed soliton is solved by using renormalization method. The effects of obliqueness (l _x ) of the wave vector, magnetic field strength (B ₀), quantum parameter for ions (H _i ), soliton velocity (θ) and Fermi temperature ratio (σ) on amplitudes and widths of the ZK-soliton and as well as of the dressed soliton are investigated. The conditions for the validity of the higher order correction are described. Suitable parameter ranges for the existence of compressive and rarefactive dressed solitons are also discussed.     

Planar and nonplanar quantum dust ion-acoustic Gardner double layers in multi-ion dusty plasma

The longitudinal fast solitary waves induced by weakly relativistic positron showers of astrophysical origin are studied in a plasma system contaminated with some massive impurities in presence of superthermal effects. The superthermal effects are due to the high energy electrons. The impurities are dust corpuscles with positive and negative charges. It is noticed that increase in the kappa parameter of electrons and relativistic streaming factor of weakly relativistic positron shower, negative dust concentration invoke an enhancement in the strength of solitary wave. On the other hand increase in the shower’s temperature as well as positive dust concentration diminish the solitary hump strength. It is worth to mention that only hump type compressive fast solitary waves are predicted by our model, for the given set of plasma parameters, because the convective coefficient of the nonlinear governing equation for solitary wave remains positive in considered regime of interaction for plasma and positron shower. Our calculations in linear regime predict both the fast and slow positron shower induced longitudinal, electrostatic perturbations. Our results may be of importance in understanding the nonlinear propagation of waves in doped astrophysical superthermal plasmas with relativistic positron showers.     

Fully nonlinear ion-acoustic solitary waves in a warm magnetized plasma with electron inertia

Ion-acoustic solitary waves in a warm, magnetized plasma with electron inertia have been investigated through Sagdeev pseudopotential method. It has been established the existence of both compressive supersonic solitons, and rarefactive subsonic and supersonic solitons within the parametric domains. The effect of the external magnetic field for generation of the supersonic compressive solitons of constant amplitudes appears to be passive after some critical direction of propagation of the wave. However, up to the critical direction of propagation, the magnetic resistance is found to be quite active to drastically reduce the soliton amplitudes. The generation of rarefactive solitons in this warm magnetized plasma is rather more feasible to be supersonic without electron inertia.     

Arbitrary amplitude ion-acoustic solitons in two-electron temperature warm ion plasma

The large amplitude Ion-acoustic solitons in collisionless plasma consisting of warm adiabatic ions, isothermal positrons and two-temperature distribution of electrons are investigated. Using pseudo-potential approach, an energy integral equation for the system has been derived which encompasses complete nonlinearity for the plasma system. The existence region of the solitons is analyzed numerically. It is found that for selected set of plasma parameters, both rarefactive and compressive solitons exist in the electron-positron-ion (EPI) plasma. It is also found that due to finite positron concentration both subsonic and supersonic rarefactive soliton exist in EPI plasma. An increase in finite ion temperature ratio decreases the amplitude of the rarefactive solitons. In the case of small amplitude, it is found that there exist supersonic compressive as well as rarefactive solitons simultaneously. The amplitude of the solitons decreases with increase in ion temperature ratio (σ), however an increase in positron concentration (α) and temperature ratio of positron to electrons (γ) increases the amplitude of the solitons. Effect of various plasma parameters on the characteristics of the solitons are discussed in detail. The results of the investigation may be helpful to understand the nonlinear structures in auroral plasma, pulsars and magnetospheric astrophysical environment as well as laboratory plasmas.     

Characteristic of ion acoustic shock waves in a dissipative quantum pair plasma with dust particulates

The behavior of quantum dust ion-acoustic (QDIA) shocks in a plasma including inertialess quantum electrons and positrons, classical cold ions and stationary negative dust grains are studied, using a quantum hydrodynamic model (QHD). The effect of dissipation due to the viscosity of ions is taken into account. The propagation of small but finite amplitude QDIA shocks is governed by the Kortoweg-de Vries-Burgers (KdVB) equation. The existence regions of oscillatory and monotonic shocks will depend on the quantum diffraction parameter (H) and dust density (d) as well as dissipation parameter (η ₀). The effect of plasma parameters (d,H,η ₀), on these structures is investigated. Results indicate that the thickness and height of monotonic shocks; oscillation amplitude of the oscillatory shock wave and it’s wavelength effectively are affected by these parameters. Additionally, the possibility of propagation of both compressive and rarefactive shocks is investigated. It is found that depending on some critical value of dust density (d _c ), which is a function of H, compressive and rarefactive shock waves can’t propagate in model plasma. The present theory is applicable to analyze the formation of nonlinear structures at quantum scales in dense astrophysical objects.     

Electrostatic compressive and rarefactive shocks and solitons in relativistic plasmas occurring in polar regions of pulsar

The electrostatic shocks and solitons are studied in weakly relativistic and collisional electron-positron-ion plasmas occurring in polar regions of pulsar. The plasma system is composed of relativistically streaming electrons, positrons while ions are taken to be stationary. Dissipative effects in the system are due to collision phenomena among the constituents of relativistic plasma. Nonlinear dynamics of the dissipation and dispersion dominated relativistic plasma systems are governed by Korteweg-de Vries Burger (KdVB) and Korteweg-de Vries (KdV) equations respectively. Numerical results, exploring the effects of plasma parameters on the profile of nonlinear waves are expedited graphically for illustration. Positron to electron temperature ratio plays the role of a decisive parameter. It is noticed that compressive shocks and solitons evolve in the system if the positron to electron temperature ratio is less than a critical value. However, there exists a threshold value of positron to electron temperature ratio beyond which the system supports the rarefactive shocks and solitons. The results may have importance in the relativistic plasmas of pulsar magnetosphere.     

Nonlinear dust acoustic waves in electronegative dusty plasmas

The problem of nonlinear localized dust acoustic (DA) is addressed in a plasma comprising positive ions, negative ions, and mobile negatively charged dust grains. We first consider the case when the grain charge remains constant and discuss later the case when the charge variations are self-consistently included. It is found that a relative increase of the positive ion density favors the propagation of the DA solitary waves, in the sense that the domain of their admissible Mach numbers enlarges. Furthermore, electronegativity makes the dust acoustic solitary structure more spiky. When the dust grain charge Q _d is allowed to fluctuate, the latter is expressed in terms of the Lambert function and we take advantage of this transcendental function to investigate the variable charge DA solitary wave. Q _d adopts a localized profile and becomes more negative as the number of charges Z ₍₋₎ of the negative ion increases. The dust grains are found to be highly localized. This localization (accumulation) caused by a balance of the electrostatic forces acting on the dust grains becomes more effective for lower values of Z ₍₋₎. An increase of Z ₍₋₎ may lead to a local depletion of the negative ions from the region of the soliton’s localization. The results are useful to understand the salient features of localization of large amplitude dust acoustic waves in cosmic plasmas such as the ionospheric D-region and the mesosphere.