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.     

Rogue wave in Titan’s atmosphere

Rogue wave in a collisionless, unmagnetized electronegative plasma is investigated. For this purpose, the basic set of fluid equations is reduced to 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 ion-acoustic wavepackets through the derivation of the nonlinear Schr?dinger (NLS) equation. In order to show that the characteristics of the rogue wave is influenced by the plasma parameters, the relevant numerical analysis of the NLS equation is presented. The relevance of our investigation to the Titan’s atmosphere is discussed.     

Dust-acoustic solitary and rogue waves in a Thomas-Fermi degenerate dusty plasma

The formation and propagation of dust-acoustic (DA) solitary and rogue waves are studied in a non-relativistic degenerate Thomas-Fermi thermal dusty plasma incorporating transverse velocity perturbation effects. The electrons and ions are described by the Thomas-Fermi density distributions, whereas the dust grains are taken as dynamic and classical. By using the reductive perturbation technique, the cylindrical Kadomtsev-Petviashvili (CKP) equation is derived, which is then transformed into a Korteweg-deVries (KdV) equation by using appropriate variable transformations. The latter admits a solitary wave solution. However, when the carrier waves frequency is much smaller than the dust plasma frequency, the DA waves evolve into the nonlinear modulation instability, generating modulated wave packets in the form of Rogue waves. For the study of DA-rogue waves, the KdV equation is transformed into a self-focusing nonlinear Schrödinger equation. The variation of dust temperature and the electron density affects the nonlinearity and dispersion coefficients which suppress the amplitudes of the DA solitary and rogue waves. The present results aim to describe the nonlinear electrostatic excitations in astrophysical degenerate dense plasma.     

Effect of nonextensive electron and ion on dust acoustic rogue waves in dusty plasma of opposite polarity

Propagation of nonlinear dust-acoustic waves in a magnetized collisionless plasma having positively, negatively charged dust grains and nonextensive distributed electrons and ions has been investigated. A reductive perturbation method is used to obtain a nonlinear Korteweg-de Vries (KdV) equation describing the model. The dynamics of the modulational instability gives rise to the formation of rogue waves that is described by a nonlinear Schrödinger equation. The dependence of rogue waves profiles on positive and negative charged dust cyclotron frequencies, nonextensive parameters of electrons and ions is investigated numerically. The result of the present investigation may be applicable to some plasma environments, such as cometary tails and upper mesosphere.     

Rogue waves for Kadomstev-Petviashvili equation in electron-positron-ion plasma

The nonlinear ion-acoustic waves in plasma having excess super-thermal electrons and positrons have been investigated. Reductive perturbation method is used to obtain a Kadomstev-Petviashvili equation describing the system. The dynamics of the modulationally unstable wave packets described by the Kadomstev-Petviashvili equation gives rise to the formation of rogue excitation that is described by a nonlinear Schrödinger equation. The dependence of rogue waves profiles on the system parameters investigated numerically. The result of the present investigation may be applicable to some plasma environments, such as galactic clusters, interstellar medium.     

Ion-acoustic rogue waves in a plasma with a q-nonextensive electron velocity distribution

Ion-acoustic rogue waves (IARWs) are addressed in a two-component plasma with a q-nonextensive electron velocity distribution. A weakly nonlinear analysis is carried out to derive a Korteweg-de Vries (K-dV) equation with a particular emphasis on its application to the IARWs. This K-dV equation is transformed to a nonlinear Schr?dinger equation, provided that the frequency of the carrier wave is much smaller than the ion plasma frequency. Interestingly, it is found that the IARWs may be drastically affected by electron nonextensivity depending on whether the entropic index q is positive or negative. In view of the crucial importance of RWs in space environments, our results should be useful in understanding the basic features of the nonextensive IARGs that may occur in space plasmas.     

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.     

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.     

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.     

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.     

The dynamo theory of plasma turbulence wave in rotating celestial bodies

The various modes of plasma turbulence waves (including MHD waves) are easily excited under cosmic circumstances. In this paper, if we consider that the celestial bodies rotate, there is a source term generated for the magnetic induced equation by the excited plasma turbulence waves. If we expand the turbulent field in the Fourier series and include rotation velocity, the dynamo equation for turbulent waves is obtained. We have also obtained the solutions of various wave forms corresponding to different rotation velocities and then we significantly discuss the magnetic fields in the Sun, planets, and other celestial bodies.     

Electron-acoustic solitary waves in a magnetized plasma with hot electrons featuring Tsallis distribution

Nonlinear dynamics of electron-acoustic solitary waves in a magnetized plasma whose constituents are cold magnetized electron fluid, hot electrons featuring Tsallis distribution, and stationary ions are examined. The nonlinear evolution equation (i.e., Zakharov–Kuznetsov (ZK) equation), governing the propagation of EAS waves in such plasma is derived and investigated analytically and numerically, for parameter regimes relevant to the dayside auroral zone. It is revealed that the amplitude, strength and nature of the nonlinear EAS waves are extremely sensitive to the degree of the hot electron nonextensivity. Furthermore, the obtained results are in good agreement with the observations made by the Viking satellite.     

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.     

Nonlinear propagation of dust ion-acoustic waves in dusty multi-ion dense plasma

We have studied the nonlinear propagation of dust ion-acoustic (DIA) waves in a dusty multi-ion dense plasma (with the constituents being degenerate, either non-relativistic or ultra-relativistic) and the propagation of such waves have been investigated by the reductive perturbation method. From the stationary solution of the Korteweg de-Vries (K-dV) equation and Burgers’ equation the nonlinear waves (specially, solitary and shock waves) have been found to be formed in the dusty plasma system under consideration. It has shown that the basic features of these waves are significantly modified by both the positive and negative ions and dust number densities, the degenerate of the constituents. The implications of our results have been briefly discussed.     

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.     

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.     

Finite orbital angular momentum states and Laguerre–Gaussian potential in two-temperature electron plasmas

Electron-acoustic waves are studied with orbital angular momentum (OAM) in an unmagnetized collisionless uniform plasma, whose constituents are the Boltzmann hot electrons, inertial cold electrons and stationary ions. For this purpose, we employ the fluid equations to obtain a paraxial equation in terms of cold electron density perturbations, which admits both the Gaussian and Laguerre–Gaussian (LG) beam solutions. Furthermore, an approximate solution for the electrostatic potential problem is found, which also allows us to express the components of the electric field in terms of LG potential perturbations. Calculating the energy flux of the electron-acoustic waves, an OAM density for these waves is obtained. Numerically, it is found that the parameters, such as, azimuthal angle, radial and angular mode numbers, and the beam waist strongly modify the LG potential profiles associated with electron-acoustic waves. The present results should be helpful to study the trapping and transportation of plasma particles and energy as well as to understand the electron-acoustic mode excitations produced by the Raman backscattering of laser beams in a uniform plasma.     

Effect of <Emphasis Type="Italic">q</Emphasis>-nonextensive distribution of electrons on electron acoustic solitons

Ion acoustic shock waves (IASWs) are studied in a plasma consisting of electrons, positrons and ions. Boltzmann distributed positrons and superthermal electrons are considered in the plasma. 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 observed that an increasing positron concentration decreases the amplitude of the waves. Furthermore, in the existence of the kinematic viscosity among the plasma, the shock wave structure appears. The effects of ion kinematic viscosity (η ₀) and the superthermal parameter (k) on the ion acoustic waves are found.     

Propagation of two dimensional cylindrical fast magnetoacoustic solitary waves in a warm dust plasma

A set of multi-fluid equations and Maxwell’s equations are carried out to investigate the properties of nonlinear fast magnetoacoustic solitary waves with the combined effects of dusty plasma pressure and transverse perturbation in the bounded cylindrical geometry. The reductive perturbation method has been applied to the dynamical system causeway and the derived two dimensional cylindrical Kadomtsev–Petviashvili equation (CKP) predicts different natures of solitons in complex plasma. Under a suitable coordinate transformation the CKP equation can be solved analytically. The change in the soliton structure due to mass of dust, ion temperature, ion density, and dust temperature is studied by numerical calculation of the CKP equation. It is noted that the dust cylindrical fast magnetoacoustic solitary waves in warm plasmas may disappear slowly because of an increase in dust mass. 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.     

Effects of nonthermal ions of distinct temperatures on dust acoustic shock waves in a dusty plasma

The nonlinear propagation of dust acoustic (DA) waves in an unmagnetized dusty plasma system consisting of negatively charged mobile dust fluid, Boltzmann distributed electrons, and two-temperature nonthermally distributed ions, is rigorously investigated. The reductive perturbation method has been employed to derive the Burgers equation. The hydrodynamic equation for inertial dust grains has been used to derive the Burgers equation. The effects of two temperature nonthermally distributed ions and dust kinematic viscosity, which are found to significantly modify the basic features of DA shock waves, are briefly discussed. Our present investigation can be effectively utilized in many astrophysical situations (e.g. satellite or spacecraft observations, Saturn’s E ring, etc.), which are discussed briefly in this analysis.