Ion acoustic solitons of KdV and modified KdV equations in weakly relativistic plasma containing nonthermal electron,positron and warm ion

In this paper, the ion-acoustic solitons in a weakly relativistic electron-positron-ion plasma have been investigated. Relativistic ions, Maxwell-Boltzmann distributed positrons and nonthermal electrons are considered in collisionless warm plasma. Using a reductive perturbation theory, a Korteweg-de Vries (KdV) equation is derived, and the relativistic effect on the solitons is studied. It is found that the amplitude of solitary waves of the KdV equation diverges at the critical values of plasma parameters. Finally, in this situation, the solitons of a modified KdV (mKdV) equation with finite amplitude is derived.     

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.     

Obliquely propagating electrostatistic solitary structures in a hot magnetized dusty plasma with vortex-like electron distribution

The nonlinear properties of solitary waves structure in a hot magnetized dusty plasma consisting of a negatively charged, extremely massive hot dust fluid, positively charged hot ion fluid and vortex-like distributed electrons, are reported. A modified Korteweg de Vries equation (mKdV) which admits a solitary wave solution for small but finite amplitude is derived using a reductive perturbation theory. The modifications in the amplitude and width of the solitary wave structures due to the inclusion of an external magnetic field and dust and ions temperature are investigated. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

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.     

Compressive and Rarefactive Dust-acoustic Solitary Structures in a Magnetized Two-ion-temperature Dusty Plasma

A rigorous theoretical investigation has been made of obliquely propagating dust-acoustic solitary structures in a cold magnetized two-ion-temperature dusty plasma consisting of a negatively charged, extremely massive, cold dust fluid and ions of two different temperatures. The reductive perturbation method has been employed to derive the Korteweg-de Vries (K-dV) equation which admits a solitary wave solution for small but finite amplitude limit. It has been shown that the presence of second component of ions modifies the nature of dust-acoustic solitary structures and may allow rarefactive dust-acoustic solitary waves (solitary waves with density dip) to exist in such a dusty plasma system. The effects of obliqueness and external magnetic field on the properties of these dust-acoustic solitary structures are also briefly discussed.     

Effects of two-temperature electrons, external oblique magnetic field, concentration of charged dust grains and higher-order nonlinearity on dust ion-acoustic solitary waves in Saturn's E-ring

The purpose of the present work is to investigate some nonlinear properties of the dust ion-acoustic (DIA) solitary waves in a four-component hot-magnetized dusty plasma consisting of charged dust grains, positively charged ions and two-temperature isothermal electrons. Applying a reductive perturbation theory, a nonlinear Korteweg-de Vries (KdV) equation for the first-order perturbed potential and a linear inhomogeneous KdV-type equation for the second-order perturbed potentials are derived. Stationary solutions of these coupled equations are obtained using a renormalization method. A method based on energy consideration is used to obtain a condition for stable solitons. The effects of two different types of isothermal electrons, external oblique magnetic field, concentration of negatively (positively) charged dust grains and higher-order nonlinearity on the nature of the DIA solitary waves are discussed. The numerical results are applied to Saturn's E-ring.     

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.     

Optical layouts of the WSO-UV spectrographs

Electron acoustic blow up solitary waves and periodic waves are studied in a classical unmagnetized plasma containing cold electron fluid, kappa distributed hot electrons and stationary ions. We obtain Korteweg-de Vries (KdV) equation for electron acoustic waves (EAWs) using the reductive perturbation technique (RPT). Applying bifurcation theory of planar dynamical systems to the obtained KdV equation, we prove the existence of electron acoustic blowup solitary and periodic wave solutions. Depending on different physical parameters, two types of exact explicit solutions of the mentioned waves are derived. Our model may be applied to explain blow up solitary and periodic wave features that may occur in the planetary magnetosphere and the plasma sheet boundary layer.     

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.     

Energy of electron acoustic solitons in plasmas with superthermal electron distribution

The propagation of nonlinear waves in plasmas consisting of cold electron fluid and superthermal hot electrons and stationary ions is studied. The Korteweg-de Vries (KdV) equation is derived using the reductive perturbation theory. It is found that only the rarefractive solitons can be created. Moreover, the linear dispersion relation and energy of solitary waves in the presence of hot superthermal electrons are derived. Our investigation is of wide relevance to astronomers and space scientists working on interstellar space plasmas.     

Bifurcations of electron acoustic traveling waves in an unmagnetized quantum plasma with cold and hot electrons

Bifurcations of nonlinear electron acoustic solitary waves and periodic waves in an unmagnetized quantum plasma with cold and hot electrons and ions has been investigated. The one dimensional quantum hydrodynamic model is used to study electron acoustic waves (EAWs) in quantum plasma. Applying the well known reductive perturbation technique (RPT), we have derived a Korteweg-de Vries (KdV) equation for EAWs in an unmagnetized quantum plasma. By using the bifurcation theory and methods of planar dynamical systems to this KdV equation, we have presented the existence of two types of traveling wave solutions which are solitary wave solutions and periodic traveling wave solutions. Under different parametric conditions, some exact explicit solutions of the above waves are obtained.     

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.     

Interaction of ion beam with dust grains produces dust-acoustic solitary waves in Herbig-Haro objects

Properties of dust-acoustic solitary waves in a warm dusty plasma are analyzed by using the hydrodynamic model for massive dust grains, electrons, ions, and streaming ion beam. For this purpose, Korteweg-de Vries (KdV) equation for the first-order perturbed potential and linear inhomogeneous KdV-type equation for the second-order perturbed potential have been derived and their analytical solutions are presented. In order to show the characteristics of the dust-acoustic solitary waves are influenced by the plasma parameters, the relevant numerical analysis of the KdV and linear inhomogeneous KdV-type equations are obtained. The dust-acoustic solitary waves, as predicted here, may be associated with the nonlinear structures caused by the interaction of polar jets with the interstellar medium, which is known as Herbig-Haro objects.     

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.     

Dust ion-acoustic solitary and shock waves in a dusty plasma with non-thermal electrons

A theoretical investigation of the one dimensional dynamics of nonlinear electrostatic dust ion-acoustic (DIA) waves in an unmagnetized dusty plasma consisting of ion fluid, non-thermal electrons and fluctuating immobile dust particles has been made by the reductive perturbation technique. The basic features of DIA solitary and shock waves are studied by deriving the Korteweg-de Vries (KdV) and KdV Burger equations, respectively. It is shown that the special patterns of nonlinear electrostatic waves are significantly modified by the presence of the non-thermal electron component. In particular, the rarefactive solitary and shock structures are found with smaller amplitude in comparison to the isothermal case. The transition from DIA solitary to shock waves is also studied which is related to the contributions of the dispersive and dissipative terms. It is found that the dust charge fluctuation is a source of dissipation, and is responsible for the formation of the dust ion-acoustic shock waves. Furthermore, the dissipative effect becomes important and may prevail over that of dispersion as the population of non-thermal electrons present decreases. The present investigation may be of relevance to electrostatic solitary structures observed in many space dusty plasma, such as Saturn’s E-ring.     

Propagation properties of ion acoustic waves in a magnetized superthermal bi-ion plasma

A theoretical investigation is carried out to analyse the propagation of ion acoustic (IA) waves in a magnetized bi-ion plasma having two populations of fluid ions and kappa-distributed electrons. The propagation properties of all possible modes (in the linear regime) are investigated. The nonlinear evolution of the IA solitary waves is governed by a Korteweg-de Vries (KdV)-like equation. The influence of obliqueness, magnitude of the magnetic field, ion polarity and electron superthermality on the IA waves is then examined. Our findings should aid in understanding the nonlinear electrostatic excitations that may propagate in spatial magnetized 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.     

Effect of nonthermality of ions on the nature of dust acoustic waves in two temperatures charged dusty grains

Effect of nonthermality of ions on the propagation of dust-acoustic waves (DAWs) in unmagnetized plasma having electrons, singly charged ions, hot and cold dust grains have been investigated. The reductive perturbation method is employed to reduce the basic set of fluid equations to the Korteweg-de Vries (KdV) equation. Moreover, the energy of two temperatures charged dusty grains were computed. The present investigation can be of relevance to the electrostatic solitary structures observed in various space plasma environments.     

Nonlinear periodic and algebraic ion-acoustic solitary waves in a relativistic plasma

We derive a mixed modified Korteweg-de Vries (MK-dV) equation from a semi-relativistic ion acoustic wave with hot ions by the fluid approximation. The positive cubic nonlinearity of the mixed MK-dV equation give rise to the periodic progressive waves and the algebraic solitary waves. The periodic wave bears a series of solitary pulses, and the algebraic solitary wave reduces the rarefactive solitary wave in the limit of the particular boundary condition. These nonlinear wave modes explain, respectively, the periodic pulse of the potential and the rarefactive solitary wave of the fine structure observed in space.