New exact solutions for nonlinear solitary waves in Thomas-Fermi plasmas with (G′/G)-expansion method

The nonlinear propagation of ion acoustic waves in an ideal plasmas containing degenerate electrons is investigated. The Korteweg-de-Vries (K-dV) equation is derived for ion acoustic waves by using reductive perturbation method. The analytical traveling wave solutions of the K-dV equation investigated, through the (G′/G)-expansion method. These traveling wave solutions are expressed by hyperbolic function, trigonometric functions are rational functions. When the parameters are taken special values, the solitary waves are derived from the traveling waves. Also, numerically the effect different parameters on these solitary waves investigated and it is seen that exist only the compressive solitary waves in Thomas-Fermi plasmas.     

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.).     

Roles of positively charged heavy ions and degenerate plasma pressure on cylindrical and spherical ion acoustic solitary waves

The properties of heavy-ion-acoustic (HIA) solitary structures associated with the nonlinear propagation of cylindrical and spherical electrostatic perturbations in an unmagnetized, collisionless dense plasma system has been investigated theoretically. Our considered model contains degenerate electron and inertial light ion fluids, and positively charged static heavy ions, which is valid for both of the non-relativistic and ultra-relativistic limits. The Korteweg-de Vries (K-dV) and modified K-dV (mK-dV) equations have been derived by employing the reductive perturbation method, and numerically examined in order. It has been found that the effect of degenerate pressure and number density of electron and inertial light ion fluids, and positively charged static heavy ions significantly modify the basic features of HIA solitary waves. It is also noted that the inertial light ion fluid is the source of dispersion for HIA waves and is responsible for the formation of solitary waves. The basic features and the underlying physics of HIA solitary waves, which are relevant to some astrophysical compact objects, are briefly discussed.     

Ion acoustic shock waves in weakly relativistic and dissipative plasmas with nonthermal electrons and thermal positrons

Propagation of ion acoustic waves in plasmas containing electrons, positrons and high relativistic ions is investigated. It is shown that the Korteweg-de Vries (KdV) equation describes the nonlinear waves in this media. The amplitude and energy of the KdV solitary waves are derived and the effects of relativistic ions on these quantities are discussed.     

Kadomtsev–Petviashvili equation for solitary waves in warm dense astrophysical electron-positron-ion plasmas

Theoretical investigation is carried out to understand the dynamics and stability of three dimensional ion solitary waves propagating in dense plasma comprising of ultra-relativistic degenerate electrons and positrons and warm ions. A linear dispersion relation is derived which shows a strong dependence of wave on positron concentration (through the change of density balance) and ion-to-degenerate electron temperature ratio. A nonlinear Kadomtsev-Petviashvili equation is derived by employing the reductive perturbation technique and solved analytically and the conditions for existence of stable solitary waves are found. The analysis reveals that only compressive solitary waves exist in the system. Effects of the change of density balance and Fermi temperature ratios are studied in detail, both analytically and numerically. Furthermore, the conditions for stable solitary waves are discussed by using energy consideration method. The numerical results are also presented by using the parameters consistent with the degenerate and ultrarelativistic astrophysical plasmas.     

Effect of the presence of excess superthermal hot electrons on electron-acoustic solitary waves in auroral zone plasma

A theoretical investigation is carried out for the nonlinear properties of small amplitude electron acoustic solitary waves (EAWs) in an unmagnetized collisionless plasma consisting of a cold electron fluid and hot electrons obeying κ velocity distribution, and stationary ions. The Korteweg de Vries (KdV) equation that contains the lowest-order nonlinearity and dispersion is derived from the lowest order of perturbation and a linear inhomogeneous (KdV-type) equation that accounts for the higher-order nonlinearity and dispersion is obtained. A stationary solution for equations resulting from higher-order perturbation theory has been found using the renormalization method. The effects of the spectral index κ and the higher-order corrections are found to significantly change the properties (viz. the amplitude, width, electric field ) of the EASWs. A comparison with the Viking Satellite observations in the dayside auroral zone are also discussed.     

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.     

Solitary and rogue waves in Fermi-Dirac plasmas: relativistic degeneracy effects

Ion acoustic (IA) solitary and rogue waves are studied in an unmagnetized plasma consisting of non-degenerate warm ions, relativistically degenerate electrons and positrons. By using the reductive perturbation technique, the evolution of IA solitary waves is described by the Korteweg-de Vries (KdV) equation. However, when the frequency of the carrier wave is much smaller than the ion plasma frequency then the KdV equation is also used to study the nonlinear evolution of modulationally unstable modified IA wavepackets through the derivation of nonlinear Schrödinger equation. It is found that the characteristics of the IA solitary and rogue waves are substantially influenced by the intrinsic plasma parameters. The relevance of the present investigation involving IA solitary and rogue waves in astrophysical plasma environments is also highlighted.     

Cylindrical and spherical ion acoustic solitary waves in electron-positron-ion plasmas with superthermal electrons

Propagation of cylindrical and spherical ion acoustic solitary waves in plasmas consisting of cold ions, superthermal electrons and thermal positrons are investigated. It is shown that cylindrical/spherical Korteweg-de-Vries equation governs the dynamics of ion-acoustic solitons. The effects of nonplanar geometry and also superthermal electrons on the characteristics of solitary wave structures are studied using numerical simulations. Obtained results are compared with the results of the other published papers and errors in the results of some papers are pointed.     

Electrostatic electron acoustic solitons in electron-positron-ion plasma with superthermal electrons and positrons

Properties of fully nonlinear electron-acoustic solitary waves in an unmagnetized and collisionless electron-positron-ion plasma containing cold dynamical electrons, superthermal electrons and positrons obeying Cairns’ distribution have been analyzed in the stationary background of massive positive ions. A linear dispersion relation has been derived, from which it is found that even in the absence of superthermal electrons, the superthermal positron component can provide the restoring force to the cold inertial electrons to excite electron-acoustic waves. Moreover, superthermal electron and positron populations seem to enhance the electron acoustic wave phase speed. For nonlinear analysis, Korteweg-de Vries equation is obtained using the reductive perturbation technique. It is found that in the presence of positron both hump and dip type solitons appear to excite. The present work may be employed to explore and to understand the formation of electron acoustic soliton structures in the space and laboratory plasmas with nonthermal electrons and positrons.     

On the head-on collision between two ion acoustic solitary waves in a weakly relativistic plasma containing nonextensive electrons and positrons

The head-on collision of two ion acoustic solitary waves propagating in opposite directions in a weakly relativistic electron-positron-ion plasma composed of weakly relativistic warm ion fluid and nonextensive electrons, positrons is investigated. Using extended Poincaré-Lighthill-Kuo method, the Korteweg-de Vries equations and the analytical phase shifts after the head-on collision of two solitary waves are derived. The effects of the nonextensive parameter, positron-to-electron density ratio, ion-to-electron temperature ratio, electron-to-positron temperature ratio and relativistic factor on the phase shifts are studied. It is found that these parameters can significantly influence the phase shifts of solitary waves.     

Contribution of Higher-Order Nonlinearity to obliquely electron-acoustic solitary waves in a magnetized auroral zone plasma

Using the Viking Satellite observations data in the dayside auroral zone, a theoretical investigation is carried out for contribution of the higher-order nonlinearity to nonlinear obliquely electron-acoustic solitary waves (EASWs) in a magnetized collisionless plasma consisting of a cold electron fluid and non-thermal hot electrons obeying a non-thermal distribution, and stationary ions. A Zakharov–Kuznetsov (ZK) equation that contains the lowest-order nonlinearity and dispersion is derived from the lowest order of perturbation and a linear inhomogeneous (ZK-type) equation that accounts for the higher-order nonlinearity and dispersion is obtained. A stationary solution for equations resulting from higher-order perturbation theory has been found using the renormalization method. The effects of the external magnetic field and the obliqueness are found to significantly change the higher-order properties (viz. the amplitude, width, electric field and energy) of the EASWs. The effect of higher-order nonlinearity on the amplitude and width of the soliton are also discussed. A comparison with the Viking Satellite observations in the dayside auroral zone are taken into account.     

Effect of high relativistic ions on ion acoustic solitons in electron-ion-positron plasmas with nonthermal electrons and thermal positrons

Propagation of ion acoustic solitary waves are studied in e-p-i plasmas containing high relativistic ions, Maxwell–Boltzmann distributed positrons and nonthermal electrons. Reductive perturbation method is used and the Korteweg-de Vries (KdV) equation is derived. The effects of high relativistic ions and nonthermal electrons on soliton characters are studied.     

Arbitrary amplitude ion-acoustic solitary waves in superthermal electron-positron-ion magnetoplasma

Arbitrary amplitude ion-acoustic solitary waves propagating in a magnetized plasma composed of positive ions, superthermal electrons and positrons are investigated. For this purpose, the ions are represented by the hydrodynamical fluid equations while the non-Maxwellian electrons and positrons densities are assumed to follow kappa (κ) distribution. The basic equations are reduced to a pseudoenergy-balance equation. Existence conditions for large amplitude solitary waves are presented. The analytical and numerical analysis of the latter show that the ion-acoustic solitary wave can propagate only in the subsonic region in our plasma system and it is significantly influenced by the plasma parameters. The present analysis could be helpful for understanding the nonlinear ion-acoustic solitary waves propagating in interstellar medium and pulsar wind, which contain an excess of superthermal particles.     

Interaction of cylindrical and spherical ion acoustic solitary waves with superthermal electrons and positrons

Interaction of nonplanar ion acoustic solitary waves is an important source of information to study the nature and characteristics of ion acoustic solitary waves (IASWs) structures. The head-on collision between two cylindrical/spherical IASWs in un-magnetized plasmas comprising with inertial ions, superthermal electrons and positrons is investigated by using the extended version of Poincaré-Lighthill-Kuo (PLK) perturbation method. It has been shown numerically that how the interactions are taking place in cylindrical and spherical geometry. The nonplanar geometry modified analytical phase shifts following the head-on collision are derived. The effects of the superthermal electrons and positrons on the phase shift are studied. It is shown that the properties of the interaction IASWs in different geometry are very different.     

Head-on collision of ion-acoustic solitary waves in magnetized plasmas with nonextensive electrons and positrons

This article presents the first study of the head-on collision of two ion-acoustic solitary waves (IASWs) in magnetized plasmas with nonextensive electrons and positrons using the extended Poincaré-Lighthill-Kuo (PLK) method. The effects of the ion gyro-frequency to ion plasma frequency ratio, the positron to ion number density ratio, the electrons temperature to positrons temperature ratio, and the nonextensive parameter q on the phase shifts are investigated. It is shown that these factors significantly modify the phase shifts.     

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.     

K-dV solitons in a magnetized dusty plasma with two distinct temperature nonextensive electrons and Maxwellian ions

Nonlinear propagation of dust-acoustic (DA) waves in a magnetized dusty plasma, consisting of negatively charged mobile dust, Maxwellian ions and two distinct temperature nonextensive electrons (following nonextensive q-distribution each), has been studied and analyzed by deriving and solving the Korteweg-de-Vries (K-dV) equation. According to the outcomes of the investigation, the basic characteristics of the DA solitary profiles are found to be strongly modified by the external magnetic field, nonextensivity of the electrons and the respective number densities of the two species of electrons. The results of this investigation can be applied in both laboratory and astrophysical plasma scenarios for understanding the basic features of the localized electrostatic dust-acoustic solitary waves (DASWs).     

Effects of two-temperature electrons, external oblique magnetic field, and higher-order nonlinearity on dust acoustic solitary waves in a dusty plasma with vortex-like ion distribution

Nonlinear properties of the dust acoustic (DA) solitary waves in a dusty plasma consisting of negatively variable-charged dust particles, vortex-like distributed ions and two-temperature isothermal electrons are reported. A reductive perturbation theory has been used to derive a modified Korteweg-de Vries (mKdV) equation for the first-order perturbed potential and a linear inhomogeneous mKdV-type equation for the second-order perturbed potential. The renormalization method is used to obtain stationary solutions of these coupled equations. The modifications in the amplitude and width of the solitary wave structure due to the inclusion of two different types of isothermal electrons, external oblique magnetic field, higher-order nonlinearity, and vortex-like distributed ions are investigated. Also a method based on energy consideration was used to obtain the stability condition. Moreover, the numerical results are applied to investigate some nonlinear characteristics of the DA solitary waves.     

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.