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.     

Korteweg-de Vries equation for ion acoustic soliton with negative ions in the presence of nonextensive electrons

Korteweg-de Vries (KdV) equation for electrostatic ion acoustic wave in a three component plasma containing positive and negative ions along with the nonextensive electrons is derived. Fast and slow ion acoustic modes which propagate with different velocities are excited. The effects of variation of quantities like q (nonextensive parameter), Q (mass ratio of positive to negative ion), μ (electron to positive ion number density ratio), θ _i (positive ion to electron temperature ratio) and θ _n (negative ion to electron temperature ratio) have been presented for fast and slow ion acoustic modes. Both compressive and rarefactive solitons are observed. It is found that the solitary excitations strongly depend on the mass and density ratios of the positive and negative ions as well as on nonextensive electron parameter.     

Ion acoustic solitary and shock waves with nonextensive electrons and thermal positrons in nonplanar geometry

The nonlinear wave structures of ion acoustic waves (IAWs) in an unmagnetized plasma consisting of nonextensive electrons and thermal positrons are studied in bounded nonplanar geometry. Using reductive perturbation technique we have derived cylindrical and spherical Korteweg-de Vries-Burgers’ (KdVB) equations for IAWs. The presence of nonextensive q-distributed electrons is shown to influence the solitary and shock waves. Furthermore, in the existence of ion kinematic viscosity, the shock wave structure appears. Also, the effects of nonextensivity of electrons, ion kinematic viscosities, positron concentration on the properties of ion acoustic shock waves (IASWs) are discussed in nonplanar geometry. It is found that both compressive and rarefactive type solitons or shock waves are obtained depending on the plasma parameter.     

KP Burgers shocks in a warm electronegative plasma with q-nonextensive distributed electrons

Nonlinear properties of ion-acoustic (IA) shock are studied by incorporating the effects of electron nonextensivity in a warm electronegative plasma, whose constituents are the inertial positive/negative ions and q-distributed electrons. For this purpose, the evolution equations are solved to obtain Kadomtsev-Petviashvili (KP) Burgers equation by using the reductive perturbation technique and its solution by the tanh method. Furthermore, the conditions for the existence of oscillatory and monotonic shocks are discussed. Numerically, it is found that IA shock propagation characteristics are significantly modified by the variation of plasma parameters, such as, the effects of electron nonextensivity, the positive and negative ion-to-electron temperature ratios (θ _i ,θ _n ), respectively. The former also affect the dispersion, dissipation and nonlinearity coefficients of the KPB equation involving the IA shocks. The present analyses could be useful for understanding the nonlinear shock wave excitations in space and laboratory plasmas, where two distinct groups of ions are present.     

Ion acoustic solitons in a nonextensive plasma with multi-temperature electrons

The properties of propagation of small amplitude ion acoustic solitary waves (IASWs) are studied in a plasma containing cold fluid ions and multi-temperature electrons (cool and hot electrons) with nonextensive distribution. Korteweg-de Vries (KdV) equation with finite amplitude is derived using a reductive perturbation method. From the solitary solutions of KdV equation, the combined effects of nonextensivity and density ratio are studied on characteristics of ion acoustic (IA) solitary waves. Positive as well as negative polarity solitons exist. Since singularity exists for A=0 so we have also derived modified Korteweg de Vries (mKdV) equation to study the solitonic solution for critical values of physical parameters (q,f,σ). The nonextensivity of electrons (via q) and density ratio of electrons and ions (via f) and temperature ratio (σ) significantly influence the characteristics of ion acoustic solitary structures.     

Two dimensional ion acoustic shocks in electron-positron-ion plasmas with warm ions,and q-nonextensive distributed electrons and positrons

Two dimensional ion acoustic shocks in electron-positron-ion (e-p-i) plasma with warm ions, and nonthermal electrons and positrons following the q-nonextensive velocity distribution are studied in the presence of weak transverse perturbations. The kinematic viscosity of warm ions is included for the dissipation in the plasma system. Kadomtsev–Petviashvili–Burgers (KPB) equation is derived by using reductive perturbation method in small amplitude limit and its analytical solution is also presented. The effects of variations of positrons concentration, q-indices of electrons and positrons, ion temperature and kinematic viscosity of ions, on the propagation characteristic of two dimensional shock profile are also discussed.     

Dust ion acoustic instability with q-distribution in nonextensive statistics

The instability of dust ion acoustic waves (DIAWs) driven by ions and electrons with different drift velocities in an unmagnetized, collisionless, isotropic dusty plasma was investigated. The electrons, ions and dust particles are assumed to be the generalized q-nonextensive distributions. The spectral indices of the q-distributions for the three plasma components are different from each other. Based on kinetic theory, the dispersion relation and the instability growth rate of DIAWs are obtained. It is found that the presence of the nonextensive distribution electrons and ions significantly modify the domain of the instability growth rate, as well as the ion-electron density ratio (ρ) and drifting-thermal velocity ratio (u _i0/v _Te ). In reverse, the index of dust grains has nearly no any effect on the instability growth rate. Furthermore, the effects of these parameters on the growth rate have also been discussed in detail.     

Overtaking collision of two ion acoustic soliton in a plasma with a q-nonextensive electron and thermal positrons

Theoretically the propagation of two ion acoustic soliton interaction in a three component collisionless unmagnetized plasma which consists of electrons, positrons and cold ions, has been investigated here by employing reductive perturbation technique. In this study, q distributed electrons and Maxwell-Boltzmann distributed positrons are considered and Korteweged-de Vries (KdV) equation is derived. The KdV equation is solved to get two soliton solution by using Hirota bilinear method. The effects of the q distributed electrons on the profiles of two soliton structures and the corresponding phase shifts are investigated. It is observed that both the nonextensive parameter (q) and the ratio of positrons density and electron density (p=n _p0/n _e0), play a significant role in the formation and existence of two soliton and also in the nature of their phase shifts.     

Detection of ionospheric perturbation due to a soft gamma ray repeater SGR J1550-5418 by very low frequency radio waves

The properties of cylindrical and spherical dust acoustic (DA) solitary and shock waves in an unmagnetized electron depleted dusty plasma consisting of inertial dust fluid and ions featuring Tsallis statistics are investigated by employing the reductive perturbation technique. A Korteweg-de Vries Burgers (KdVB) equation is derived and its numerical solution is obtained. The effects of ion nonextensivity and dust kinematic viscosity on the basic features of DA solitary and shock waves are discussed in nonplanar geometry. It is found that nonextensive nonplanar DA waves behave quite differently from their one-dimensional planar counterpart.     

Propagation and interaction of dust acoustic multi-soliton in dusty plasmas with q-nonextensive electrons and ions

The nonlinear propagation and interaction of dust acoustic multi-soliton in a four component dusty plasma which consists of negatively and positively charged cold dust fluids, q-nonextensive velocity distributed electrons and ions, have been studied. Applying reductive perturbation technique (RPT), we have derived Korteweged-de Vries (KdV) equation for our model. By using Hirota bilinear method, we have obtained two-soliton and three-soliton solutions of the obtained KdV equation. Phase shifts of two-soliton and three-soliton have been presented. It has been observed that the parameters α ₁, α ₂, nonextensive parameter q, temperature ratio of ion to electron (σ), and μ play a crucial role in the formation of two-soliton and three-soliton. The implications of our results in understanding the localized nonlinear electrostatic perturbations observed in double-plasma machines, Cometary tails, Jupiter’s magnetosphere etc., where population of q-nonextensive velocity distributed electrons and ions can significantly dominate the wave dynamics, 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.     

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.     

Astrophysical naturally moderated classical positron beam interaction with nonlinear waves in nonextensive astrophysical plasmas

The positron acoustic shock and solitary wave are explored in nonextensive electron-positron-ion plasma. The plasma system under-consideration, consists of a classical positron beam, q distributed electrons and positively charged bulky ions constitute a neutralizing background. The nonlinear Korteweg-de Vries and Burger equations are derived by employing the standard reductive perturbation method. The positron acoustic wave in linear limit is also discussed for dissipative as well as nondissipative cases of nonextensive plasmas. The plasma parameters such as, the concentration of neutralizing ions background, beam velocity, temperature and q parameter of the nonextensive electrons are noticed to significantly affect the positron acoustic shock and solitary waves. Our findings may be helpful in the understanding of laboratory beam plasma interaction experiments as well as the astrophysical nonextensive plasmas interacting with positron beam.     

Obliquely propagating solitary wave structures in nonextensive magneto-rotating plasmas

The propagation of the nonlinear electrostatic ion acoustic solitary wave structures in two component, non relativistic, homogenous, magneto rotating plasma are studied. The inertialess electrons are assumed to follow nonextensive q velocity distribution. Small amplitude reductive perturbation technique is applied to derive Korteweg de Vries (KdV) equation and its analytical solution is presented. The effects of variation of different plasma parameters on propagation characteristics of solitary wave structure in the presence of the Coriolis force are discussed. It is observed that nonextensive parameter q modifies the structure of solitary wave structures in rotating plasmas.     

Effect of q-nonextensive distribution of electrons on dust-ion acoustic solitons

Properties of dust-ion acoustic solitary waves (DIASWs) in dusty plasmas composed of nonextensive electrons, cold fluid ions and stationary dust particles are investigated. The possibility of soliton formation and the effect of nonextensivity of the electron distribution on the soliton characters are studied using the pseudo-potential method. Regions of parameters in which a solitary wave can be propagated in the plasma is analyzed too. It is found that the solitary excitations strongly depend on the electron-ion density ratio (μ), Mach numbers (M) as well as the nonextensive parameter (q). It is shown that the domain of allowed Mach numbers depends drastically on the plasma parameters and especially on the electron nonextensivity. It is found that beyond a threshold value of the nonextensive parameter (q), dust-ion acoustic solitons are admitted.     

Ion acoustic solitary waves in a weakly relativistic plasma with <Emphasis Type="Italic">q</Emphasis>-nonextensive electrons and thermal positrons

Nonlinear ion acoustic solitary waves (IASWs) are addressed in a weakly relativistic plasma consisting of cold ion fluid, q-nonextensive electron velocity distribution and Boltzmann distributed positron. The Korteweg-de Vries- (KdV) equation is derived by reductive perturbation method. We investigate the effect of nonextensive electrons on solitary waves in this medium. It is found that only compressive solitons can be appeared in the existence of nonextensive electrons. It is shown that the structure of soliton depend sensitively on the q-nonextensive parameter.     

Electrostatic shock structures in a multi-species nonthermal dusty plasma

Propagation of the dust-acoustic shock waves (DASWs) in a dusty plasma containing arbitrarily charged dust, positive and negative ions following nonthermal (Cairn’s) distribution, and electrons following q-(nonextensive) distribution, has been investigated. The reductive perturbation technique is used to derive the Burgers equation for dust’s fluid dynamics. The basic features (viz. polarity, amplitude, speed, etc.) of DASWs are found to be significantly modified due to the effects of arbitrarily charged dust, number density and temperatures of heavier/lighter ions, nonextensive electrons, and dust kinematic viscosity. The present investigation can be very effective for understanding the nonlinear characteristics of the DASWs in space and laboratory dusty plasmas.     

Effect of <Emphasis Type="Italic">q</Emphasis>-nonextensive distribution of electrons on ion acoustic shock waves in dissipative plasma

Ion acoustic shock waves (IASWs) are studied in a plasma consisting of nonextensive electrons and ions. The dissipation is taken into account the kinematic viscosity among the plasma constituents. The Korteweg-de Vries-Burgers (KdV-Burgers) equation is derived by reductive perturbation method. Shock waves are solutions of KdV-Burgers equation. It is shown that acceptable values of q-parameter (where q stands for the electron nonextensive parameter) are more than 3 in a weakly nonlinear analysis. We have found that the amplitude of shock waves decreases by an increasing q-parameter.     

Shock waves in a dusty plasma having q-nonextensive electron velocity distribution

The dust-acoustic shock waves have been theoretically investigated using reductive perturbation technique. An unmagnetized four-component dusty plasma system consisting of nonextensive q-distributed electrons, Boltzmann distributed ions, and negatively as well as positively charged dust particles has been considered. The solution of Burgers equation in planar geometry is numerically analyzed. It has been observed that the nonextensive q-distribution of electrons has a significant role in the formation of shock waves. The relevance of our results to astrophysics as well as laboratory plasmas are briefly discussed.     

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.