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.     

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.     

Superthermal effect of electrons on nonplanar dust-ion-acoustic solitary waves and double layers in a dusty plasma

The basic features of planar and nonplanar time-dependent dust-ion-acoustic (DIA) solitary waves (SWs) and double layers (DLs) have been studied in an unmagnetized dusty plasma system consisting of positively and negatively charged dust, Boltzmann distributed ions and superthermal electrons (represented by kappa distribution). Using the reductive perturbation technique (RPT) we have derived modified Gardner (MG) equation, which gives information beyond the Korteweg-de Vries (KdV) limits (corresponding to the vanishing of nonlinear coefficient of the KdV equation). It is seen that the properties of nonplanar DIA SWs and DLs are significantly differs as the value of spectral index kappa (κ) changes. The present investigation may have relevance in the study of propagation of DIA waves in space and laboratory plasmas.     

Nonplanar ion-acoustic Gardner solitons in a pair-ion plasma with nonextensive electrons and positrons

The properties of nonplanar (cylindrical and spherical) ion-acoustic solitary waves (IA SWs) in an unmagnetized, collisionless electron-positron-ion (e-p-i) plasma, whose constituents are q-distributed electrons and positrons and inertial ions, are investigated by deriving the modified Gardner (MG) equation. The well known reductive perturbation method is employed to derive the MG equation. The basic features of nonplanar IA Gardner solitons (GSs) are discussed. It is found that the properties of nonplanar IA GSs (rarefactive and compressive) are significantly affected by the particle nonextensivity.     

Time dependent cylindrical and spherical DIA solitary waves with two populations of thermal electrons in dusty plasma

The propagation of Gardner solitons (GSs) in a nonplanar (cylindrical and spherical) geometry associated with a dusty plasma whose constituents are non-inertial negative static dust, inertial ions, and two population of Boltzmann electrons with two distinctive temperatures, are investigated by deriving the modified Gardner (mG) equation using the reductive perturbation method. The basic features of nonplanar dust-ion-acoustic GSs are analyzed by numerical solutions of mG equation. It has been found that the basic characteristics of GSs, which are shown to exist for the values of μ _c =n _e10/n _i0 around 0.319 for n _e20/n _i0=0.04 and T _e1/T _e2=0.2 [where n _e10 (n _e20) is the cold (hot) electron number density at equilibrium, T _e1 (T _e2) is the temperature of the cold (hot) electron species] are different from those of K-dV (Korteweg-de Vries) solitons, which do not exist around μ _c ?0.319. The implications of our results in understanding the nonlinear electrostatic perturbations observed in many laboratory and astrophysical situations (viz. double-plasma machines, rf discharge plasma, noctilucent cloud region in Earth’s atmosphere, source regions of Auroral Kilometric Radiation, Saturn’s E-ring, etc.) where electrons with different temperatures can significantly modify the wave dynamics, are also briefly discussed.     

Planar electron-acoustic solitary waves and double layers in a two-electron-temperature plasma with nonthermal ions

A rigorous theoretical investigation of nonlinear electron-acoustic (EA) waves in a plasma system (containing cold electrons, hot electrons obeying a Boltzmann distribution, and hot ions obeying a nonthermal distribution) is studied by the reductive perturbation method. The modified Gardner (MG) equation is derived and numerically solved. It has been found that the basic characteristics of the EA Gardner solitons (GSs), which are shown to exist for α around its critical value α _c [where α is the nonthermal parameter, α _c is the value of α corresponding to the vanishing of the nonlinear coefficient of the Korteweg-de Vries (K-dV) equation, e.g. α _c ≃0.31 for μ=n _h0/n _i0=0.5, σ=T _h /T _i =10, n _h0, n _i0 are, respectively, hot electron and nonthermal ion number densities at equilibrium, T _h (T _i ) is the hot electron (ion) temperature], are different from those of the K-dV solitons, which do not exist for α around α _c , and mixed K-dV solitons, which are valid around α∼α _c , but do not have any corresponding double layers (DLs) solution. The parametric regimes for the existence of the DLs, which are found to be associated with positive potential, are obtained. The present investigations can be observed in various space plasma environments (viz. the geomagnetic tail, the auroral regions, the cusp of the terrestrial magnetosphere, etc.).     

K-dV and mK-dV equations for solitary waves in negative ion plasmas with non-Maxwellian electrons

Ion-acoustic (IA) solitons in a collisionless plasma consisting of positive and negative ions and superthermal electrons are studied by using the reductive perturbation method. The basic set of fluid equations is reduced to Korteweg-de Vries (K-dV) and modified Korteweg-de Vries (mK-dV) equations. It is found that both compressive and rarefactive solitons can be propagated in this system. Also it is shown that at critical concentration of positive ions mK-dV solitons coexist. The effects of spectral index kappa, positive to negative ion density ratio and mass ratio of positive to negative ions on IA solitons structure are also 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.     

Dust ion acoustic (DIA) solitary waves in plasmas with weak relativistic effects in electrons and ions

In the new investigation of dust-ion acoustic (DIA) waves with negative dust charges and weakly relativistic ions and electrons in the plasma, compressive and rarefactive DIA solitons of interesting characters are established through the Korteweg-de Vries (KdV) equation. Eventually, the amplitudes of the compressive DIA solitons are found to be constant at some critical temperature ratio α _c (electron to ion temperature ratio) identifying some critical dust charge Z _dc . It is predicted, that the reception of dust charges by the plasma particles at the variation of temperature starts functioning to the growth of compressive soliton’s constant stage of amplitude after the state of critical α _c . The identification of critical dust charge (Z _dc ) which is found to be very great for solitons of constant amplitudes becomes feasible for very small dust to ion density ratio (σ). But it can be achieved, we observe, due to the relativistic increase in ion-density as in mass, which is also a salient feature of this investigation.     

Effect of dust polarity on dust ion-acoustic localized structures in a superthermal dusty plasma

The effects of dust polarity and superthermal electrons are incorporated in the study of dust ion-acoustic (DIA) solitary waves (SWs) as well double layers (DLs) in a dusty plasma containing warm adiabatic ions, superthermal electrons, and arbitrarily (positively or negatively) charged immobile dust. Based on the energy-like integral equation, a new relationship between the localized electrostatic disturbances and dust polarity is derived. It is shown that there exists rarefactive SWs and DLs with qualitatively different structures in a way that depends on the population of superthermal electrons. As the electrons evolve their thermodynamic equilibrium, the localized structures are found with larger amplitude. It is also found that their amplitude increases (decreases) with the increase in the negative (positive) dust number density.     

Nonlinear propagation of ion-acoustic waves in an electron-positron-ion plasma

A theoretical investigation has been made of electrostatic solitary structures in an electron-positron-ion (e-p-i) plasma, taking nonextensive electrons and nonextensive positrons. By employing the reductive perturbation method, the basic characteristics of ion-acoustic (IA) solitary waves (SWs) in a three-component e-p-i plasma (consisting of negatively charged nonextensive electrons, positively charged nonextensive positrons, and ions) have been addressed. The Korteweg-de Vries (K-dV), modified K-dV (mK-dV), and Gardner equations are derived and their numerical solutions are obtained. It has been shown that the combined effects of electron nonextensivity, positron nonextensivity, and ions significantly modify the behavior of these electrostatic solitary structures that have been found to exist with positive and negative potential in this plasma model. The present analysis may be useful to understand and demonstrate the dynamical properties of IA SWs in different astrophysical and cosmological scenarios (viz. stellar polytropes, hadronic matter and quark-gluon plasma, protoneutron stars, dark-matter halos, etc.).     

Cylindrical and spherical positron-acoustic Gardner solitons in electron-positron-ion plasmas with nonthermal electrons and positrons

A theoretical investigation has been performed on the nonlinear propagation of nonplanar (cylindrical and spherical) Gardner solitons (GSs) associated with the positron-acoustic (PA) waves in a four component plasma system consisting of nonthermal distributed electrons and hot positrons, mobile cold positrons, and immobile positive ions. The well-known reductive perturbation method has been employed to derive the modified Gardner (MG) equation. The basic features (viz. amplitude, polarity, speed, etc.) of nonplanar PA Gardner solitons (GSs) have been examined by the numerical analysis of the MG equation. It has been observed that the properties of the PA GSs in a nonplanar geometry differ from those in a planar geometry. It has been also investigated that the presence of nonthermal (Cairns distributed) electrons and hot positrons significantly modify the amplitude, polarity, speed, and thickness of such PA GSs. The results of our investigation should play an important role in understanding various interstellar space plasma environments as well as laboratory plasmas.     

New characteristics of double layers in two-temperature Lorentzian plasmas

Double layers (DLs) structures in a collisionless Lorentzian plasma consisting of warm ions and two-temperature superthermal electrons are studied by using the reductive perturbation method. The basic set of fluid equations is reduced to extended Korteweg-de Vries (EK-dV) equation. It is shown that in temperatures lower than critical value for densities around first critical concentrations of cold electrons ( \(d \to d_{c_{1}}\) ) DL structures coexist. The effects of cold to hot electron density ratio d, cold to hot electrons temperature ratio σ, spectral index of cold and hot electrons κ _c and κ _h , ion temperature δ on DLs structure are also, discussed.     

Higher-order corrections to ion acoustic waves in degenerate electron-positron-ion plasmas

The nonlinear propagation of ion acoustic waves in ideal plasmas consisting of degenerate electrons and positrons, and isothermal ions is investigated. The Korteweg de Vries (K-dV) equation that contains the lowest order nonlinearity and dispersion is derived from the lowest order of perturbation and a linear inhomogeneous (K-dV type) equation that accounts for the higher order nonlinearity and the dispersion relation is obtained. The stationary wave solution for these equations has been found using the renormalization method. Also, the effects of electrons and positrons densities and ion temperature on the amplitude and width of solitary waves are investigated, numerically. It is seen that higher order corrections significantly change the properties of the K-dV solitons. Also, it is found that both compressive and rarefactive solitary waves can be propagated in such plasma system.     

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.     

Dust-acoustic solitary waves and double layers with two temperature ions in a nonextensive dusty plasma

Small amplitude dust-acoustic solitary waves in an unmagnetized dusty plasma consisting of electrons and two temperature ions obeying the q-nonextensive distribution are investigated. Employing reductive perturbation method, the Korteweg-de Vries (KdV) equation is derived. From the solitonic solutions of KdV equation, the influence of nonextensivity of electrons as well as ions and dust concentration on the amplitude and width of dust-acoustic solitary waves has been studied. It is observed that both positive and negative potential dust acoustic solitary waves occur in this case. The modified KdV (mKdV) equation is derived in order to examine the solitonic solutions for the critical plasma parameters for which KdV theory fails. The parametric regimes for the existence of mKdV solitons and double layers (DLs) have also been determined. Positive potential double layers are found to occur in the present study.     

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.     

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.     

Nonplanar solitons in a warm electronegative plasma with electron nonextensivity effects

The nonlinear propagation of ion-acoustic waves is studied in an unmagnetized collissionless electronegative plasma, whose constituents are the inertial warm positive/negative ions and q-distributed nonextensive electrons. The latter have strong impact on the linear dispersion relation. However, for nonlinear analysis, a reductive perturbation technique is employed to derive a Korteweg-de Vries (KdV) equation accounting for nonthermal electrons in nonplanar geometries. Numerically, the effects of various plasma parameters, such as, the nonextensive parameter (q), the negative-to-positive ion mass ratio (α), the electron-to-positive ion number density ratio (μ), the positive ion-to-electron temperature ratio (θ _i ) and negative ion-to-electron temperature ratio (θ _n ), have been examined on the nonplanar compressive/rarefactive fast ion-acoustic solitons (where the wave phase speed is taken as λ>1). The relevance of our findings involving plasma wave excitations should be useful both for space and laboratory plasmas, where two distinct groups of ions besides the electrons, are present.