Thermal Effects on K-dV Solitons Existing at the Critical Density of Negative Ions in Ion-Beam Plasmas

Ion-acoustic solitons in a generalized multicomponent plasma are studied through the derivation of Korteweg-de Vries (K-dV) equation. The negative ions and ion-beams play quantitatively various roles on the existence of solitons in the plasma. Especially, the critical density introduced by the negative ions exhibits the existence of a large amplitude soliton in plasmas and due to which a derivation of a modified K-dV (mK-dV) equation is needed. By taking the higher order nonlinearity in the plasma, the transition of the K-dV equation to the mK-dV equation is also shown. Moreover, various models of the plasma due to the non-isothermality are also considered in the discussions. Further study closely related to the stability of the soliton is made and yields the salient features of the solitons.     

Ion-acoustic solitons in an inhomogeneous multicomponent plasmawith negative ions

Ion-acoustic solitary waves are studied in an inhomogeneous multicomponent plasma by the augmentation of a K-dV equation wherein a simple form of ionization has been taken to show its interaction in changing the salient features of the soliton, as compared to those observed in a homogeneous plasma. As expected, the negative ions in the plasma bring a drastic alteration on the ion-acoustic solitons, thereby establishing a new era by showing the solitary waves to be studied by a modified K-dV equation. The emphasis has been on determining how the ionization and density gradient in the inhomogeneous plasma affect the solitons     

Propagation of solitary waves in relativistic plasmas

By applying a reductive perturbation technique to the basic system of equations governing the plasma dynamics, a modified Korteweg-de Vries (K-dV) equation has been derived in relativistic plasma that includes cold ions and warm nonisothermal electrons. By reducing the effect of nonisothermality, the authors demonstrate the modification of the K-dV equation into different forms which show how to link the behavior of ion-acoustic waves in nonisothermal plasmas with that in isothermal plasmas     

Korteweg-De Vries Equation for Non-Linear Ion-Acoustic Waves in a Plasma with Negative Ions

The theoretical analysis, based on the perturbation technique, of ion-acoustic waves in the vicinity of a Korteweg-de Vries (K-dV) equation derived in a plasma with some negative ions has been made. The investigation shows that the negative ions in plasma with isothermal electrons introduced a critical concentration at which the ion-acoustic wave plays an important role of wave-breaking and forming a precursor while the plasma with non-isothermal electrons has no such singular behaviour of the wave. These two distinct features of ion waves lead to an overall different approach of present study of ion-waves. A distinct feature of non-uniform transition from the nonisothermal case to isothermal case has been shown. Few particular plasma models have been chosen to show the characteristics behaviour of the ion-waves existing in different cases.     

A numerical study of the transient behaviors of solitary waves inrelativistic plasmas

The authors study the transient behaviors of solitary waves in a relativistic plasma with nonisothermal electrons. In particular, the modified Korteweg-de Vries (K-dV) equation is solved numerically with a Gaussian function as the initial condition. In addition, it is found that the time evolution of solitons from the initial profile is quite similar to that of a K-dV equation with the exception that the soliton speeds are faster. It is also found that the relativistic ions and the nonisothermal electrons tend to have a similar effect on the soliton behavior of the wave, making nonisothermal electrons more noticeable     

Solitary Potential in a Space Plasma Containing Dynamical Heavy Ions and Bi-Kappa Distributed Electrons of Two Distinct Temperatures

The heavy ion-acoustic solitary waves(HIASWs) in a magnetized, collisionless, space plasma system(containing dynamical heavy ions and bi-kappa distributed electrons of two distinct temperatures) have been theoretically investigated. The Korteweg-de Vries(K-dV), modified K-dV(MK-dV), and higher-order MK-dV(HMK-dV) equations are derived by employing the reductive perturbation method. The basic features of HIASWs(viz. speed, polarity,amplitude, width, etc.) are found to be significantly modified by the effects of number density and temperature of different plasma species, and external magnetic field(obliqueness). The K-dV and HM-Kd V equations give rise to both compressive and rarefactive solitary structures, whereas the MK-dV equation supports only the compressive solitary structures. The implication of our results in some space and laboratory plasma situations are briefly discussed.     

Ion acoustic solitary waves in density and temperature gradients

The propagation of ion-acoustic K-dV solitary waves in weakly inhomogeneous, collisionless plasmas with gradients both in the density and the temperature of the ions has been considered. The electrons are assumed to be hot and isothermal, and the ions to be warm and adiabatic. The reductive perturbation analysis of the fluid equations is then carried out. The zero order quantities existing in the system due to the presence of the inhomogeneities are taken into account consistently and a set of ‘stretched coordinates’ appropriate for the inhomogeneous system is employed. A more general modified K-dV equation has been derived and its soliton solution is obtained explicitly. It is shown that as the soliton propagates along the temperature gradient, its amplitude and the velocity decrease, and the width increases. Further, it is found that when the two gradients are in opposite directions, the amplitude of the soliton remains constant.     

Aspect of K-dV Solitons Studied with Different Stretching Co-ordinates

The present study focusses on the conspicuous properties of the temporal and spatial K-dV solitary waves obtainable by the use of different stretching co-ordinates. Singularities are observed in solitary waves which are due to the presence of negative ions and multiple electron-temperatures in the plasmas. It is discussed how those situations are tackled by the derivation of modified K-dV equations to describe the evolution of propagating solitons. Moreover, the soliton profiles admit the interactions of negative ions and multiple electron-temperatures, which are playing the role of creating the steepness in soliton profiles. Simultaneously more solitary waves follow therein resembling the evolution of experimentally observed soliton characteristics and finally indicating the possible interest to put forth for experimental plasma investigations.     

New analytical solutions for propagation of small but finite amplitude ion-acoustic waves in a dense plasma

Abstract

The theoretical and numerical studies have been investigated on the nonlinear propagation of electrostatic ion-acoustic waves (IAWs) in an un-magnetized Thomas–Fermi plasma system consisting of electron, positrons, and positive ions for both of ultra-relativistic and non-relativistic degenerate electrons. Korteweg-de Vries (K-dV) equation is derived from the model equations by using the well-known reductive perturbation method. This equation is solved by employing the generalized Riccati equation mapping method. The hyperbolic functions type solutions to the K-dV equation are only considered for describing the effect of plasma parameters on the propagation of electrostatic IAWs for both of ultra-relativistic and non-relativistic degenerate electrons. The obtained results may be helpful in proper understanding the features of small but finite amplitude localized IAWs in degenerate plasmas and provide the mathematical foundation in plasma physics.     

Korteweg — de Vries solitons with different co-ordinate stretchings

The differences between the soliton solutions of the K-dV equation for a homogeneous, collisionless plasma, consisting of cold ions and isothermal electrons arising due to the two different sets of stretched co-ordinates have been discussed. In particular, the differences between the amplitudes and the widths of the solitons and their variations with the soliton velocity have been indicated. Further, the experimental implications of these differences and also of the two sets of stretched co-ordinates have been discussed.     

Roles of Superthermal Electrons and Adiabatic Heavy Ions on Heavy-Ion-Acoustic Solitary and Shock Waves in a Multi-Component Plasma

Heavy-ion-acoustic (HIA) waves in an unmagnetized collisionless plasma system comprising superthermal electrons, Boltzmann distributed light ions, and adiabatic positively charged inertial heavy ions have been investigated both numerically and analytically. The well-known reductive perturbation method has been used to derive the Korteweg-de Vries (K-dV) and Burgers (BG) equations. The parametric regimes for the existence of both the positive and negative solitary and shock waves have been obtained. The effects of adiabaticity of heavy ions and superthermality of electrons, which are found to notably modify the fundamental features (viz. polarity, amplitude, phase speed, etc.) of HIA solitary and shock waves, are precisely studied. The results of our theoretical investigation can be applicable to understand the characteristics and basic nonlinear structures of HIA waves both in space and laboratory plasma situations.     

Spherical Solitons in Ion-Beam Plasma

By using the reductive perturbation technique, the soliton solution of an ion-acoustic wave radially ingoing in a spherically bounded plasma consisting of ions and ion-beams with multiple electron temperatures is obtained. In sequel to the earlier investigations, the solitary waves are studied as usual through the derivation of a modified Korteweg-de Vries (K-dV) equation in different plasma models arising due to the variation of the isothermality of the plasmas. The characteristics of the solitons are finally compared with those of the planar and the cylindrical solitons.     

Head-on Collision of Ion-acoustic Multi-Solitons in e-p-i Plasma

The propagation and interaction between ion acoustic multi-solitons in an unmagnetized multicomponent plasma consisting of fluid hot ions, positrons and both hot and cold electrons, are investigated by employing the extended Poincare–Lighthill–Kuo(PLK) method. Two different Kortewege-de Vries(K-dV) equations are derived. The Hirota's method is applied to get the K-dV multi-solitons solution. The phase shift due to the overtaking and head- on collision of the multi-solitons is obtained.     

K-dV Solitons and corresponding Double Layer Phenomena in a Plasma with Multiple Electron-Temperatures

In this paper, the various conditions under which the K-dV solitons and double layers may be formed in a plasma that includes two electron-temperatures are examined by deriving a “Further modified K-dV” (FmK-dV) equation in three dimensional space in which there is assumed to be an ambient magnetic field. Structural forms of the various ion-acoustic waves are discussed by obtaining both soliton-specific and double layer-specific solitons of the FmK-dV equation. Particular results are deduced as special cases of the more general cases.     

Hamiltonian systems with indefinite kinetic energy

Some interesting features of a class of two-dimensional Hamiltonians with indefinite kinetic energy are considered. It is shown that such Hamiltonians cannot be reduced, in general, to an equivalent dynamical Hamiltonian with positive definite kinetic energy quadratic in velocities. Complex nonlinear evolution equations like the K-dV, the MK-dV and the sine-Gordon equations possess such Hamiltonians. The case of complex K-dV equation has been considered in detail to demonstrate the generic features. The two-dimensional real systems obtained by analytic continuation to complex plane of one-dimensional dynamical systems are also discussed. The evolution equations for nonlinear, amplitude-modulated Langmuir waves as well as circularly polarized electromagnetic waves in plasmas, are considered as illustrative examples.     

Electrostatic Solitary Structures in a Relativistic Degenerate Multispecies Plasma

The nonlinear propagation of cylindrical and spherical modified ion-acoustic (mIA) waves in an unmagnetized, collisionless, relativistic, degenerate multispecies plasma has been investigated theoretically. This plasma system is assumed to contain both relativistic degenerate electron and positron fluids, nonrelativistic degenerate positive and negative ions, and positively charged static heavy ions. The restoring force is provided by the degenerate pressures of the electrons and positrons, whereas the inertia is provided by the mass of positive and negative ions. The positively charged static heavy ions participate only in maintaining the quasi-neutrality condition at equilibrium. The nonplanar K-dV and mK-dV equations are derived by using reductive perturbation technique and numerically analyzed to identify the basic features (speed, amplitude, width, etc.) of mIA solitary structures. The basic characteristics of mIA solitary waves are found to be significantly modified by the effects of degenerate pressures of electron, positron, and ion fluids, their number densities, and various charge states of heavy ions. The implications of our results to dense plasmas in astrophysical compact objects (e.g., nonrotating white dwarfs, neutron stars, etc.) are briefly mentioned.     

电子束丝化扰动的孤立波解

本文用约化扰动方法讨论了与电子束丝化扰动相关的孤立波,导出了束电子密度扰动所满足的K-dV方程。 关键词：     

Effect of Bohm quantum potential in the propagation of ion–acoustic waves in degenerate plasmas

A theoretical investigation has been carried out on the propagation of the ion–acoustic(IA) waves in a relativistic degenerate plasma containing relativistic degenerate electron and positron fluids in the presence of inertial non-relativistic light ion fluid. The Korteweg-de Vries(K-dV), modified K-dV(m K-dV), and mixed m K-dV(mm K-dV) equations are derived by adopting the reductive perturbation method. In order to analyze the basic features(phase speed, amplitude, width,etc.) of the IA solitary waves(SWs), the SWs solutions of the K-dV, m K-dV, and mm K-d V are numerically analyzed. It is found that the degenerate pressure, inclusion of the new phenomena like the Fermi temperatures and quantum mechanical effects(arising due to the quantum diffraction) of both electrons and positrons, number densities, etc., of the plasma species remarkably change the basic characteristics of the IA SWs which are found to be formed either with positive or negative potential. The implication of our results in explaining different nonlinear phenomena in astrophysical compact objects, e.g.,white dwarfs, neutron stars, etc., and laboratory plasmas like intense laser–solid matter interaction experiments, etc., are mentioned.     

On the existence of ion-acoustic solitary waves in a gravitating dusty plasma having charge fluctuation

Theoretical investigation on the propagation of ion-acoustic waves in an unmagnetized self-gravitating plasma has been made for the existence of solitary waves using the reductive perturbation method. It is observed that nonlinear excitations follow a coupled third-order partial differential equation which is slightly different from the usual case of coupled Korteweg-de Vries (K-dV) system. It appears that the system so deduced is a two-component generalization of the previous one derived by Paul et al. (1999) in which it was shown that ion-acoustic solitary waves can not exist in such system.     

Solitary self-gravitational potential in magnetized astrophysical degenerate quantum plasmas

A rigorous theoretical investigation has been conducted on solitary self-gravitational potential structures in a magnetized degenerate quantum plasma system (containing heavy nuclei and degenerate electrons). The reductive perturbation method has been used 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, for the first time, that the periodic U-shaped structures represented by secant square function [Asaduzzaman et al, Physics of Plasmas, 24 , 052102 (2017)] are converted into solitary self-gravitational potential structures represented by hyperbolic secant square function due to the presence of a static external magnetic field. It is also observed that the effects of the static external magnetic field and obliqueness significantly modify the basic properties (viz. amplitude, width, speed, etc.) of the solitary self-gravitational potential structures.