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.     

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     

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.     

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.     

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.     

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.     

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.     

Ion-Acoustic Solitary Waves in Multicomponent Plasmas with Negative Ions

By using the perturbation technique, a Kortewege-de-Vries (K-dV) equation for a multicomponent plasma with negative ions and isothermal electrons has been derived. We have discussed the stationary solutions of K-dV equation and it has shown that in the presece of multiple ions, the amplitude of solitons exhibits interesting behaviour, especiallY when the negative ions are present.     

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.     

Nonlinear propagation of ultra-low-frequency electromagnetic modes in a magnetized dusty plasma

A theoretical investigation has been made of nonlinear propagation of ultra-low-frequency electromagnetic waves in a magnetized two fluid (negatively charged dust and positively charged ion fluids) dusty plasma. These are modified Alfvén waves for small value of and are modified magnetosonic waves for large , where is the angle between the directions of the external magnetic field and the wave propagation. A nonlinear evolution equation for the wave magnetic field, which is known as Korteweg de Vries (K-dV) equation and which admits a stationary solitary wave solution, is derived by the reductive perturbation method. The effects of external magnetic field and dust characteristics on the amplitude and the width of these solitary structures are examined. The implications of these results to some space and astrophysical plasma systems, especially to planetary ring-systems, are briefly mentioned. Received 8 July 1999 and Received in final form 11 October 1999     

Head-on collision of ion-acoustic solitary waves in an unmagnetized electron-positron-ion plasma

The head-on collision between two ion-acoustic solitary waves in an unmagnetized electron-positron-ion plasma has been investigated. By using the extended Poincaré-Lighthill-Kuo perturbation method, we obtain the KdV equation and the analytical phase shift after the head-on collision of two solitary waves in this three-component plasma. The effects of the ratio of electron temperature to positron temperature, and the ratio of the number density of positrons to that of electrons on the phase shift are studied. It is found that these parameters can significantly influence the phase shifts of the solitons. Moreover, the compressive solitary wave can propagate in this system.     

Effect of Second Nonthermal Ion on the Characteristics of Dust Acoustic Solitary Waves in a Magnetized Dusty Plasma with Variable Dust Charge

The nonlinear dust acoustic solitary waves in a magnetized dusty plasma with nonthermal ions and variable dust electric charge is studied analytically. Using reductive perturbation method the Zakharov‐Kuznetsov (ZK) equation is derived and effect of nonthermal coefficient, external magnetic field, and variable dust electric charge on the amplitude and width of soliton in dusty plasma is investigated. With increasing the rate of dust charge variation with respect of plasma potential, the amplitude of generated solitary waves in magnetized dusty plasma increases to a constant magnitude while its width decreases. Increasing the nonthermal ions coefficient leads to a noticeable decrease in the amplitude of solitons while the width of soliton increases. The amplitude of generated solitary waves in such a dusty plasma is independent of applied external magnetic field but we will have more localized solitons with increasing the external magnetic field strength. It is found that solitons are strongly influenced by the direction of external magnetic field. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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     

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.     

Solitons in a relativistic plasma with negative ions

The interaction of the nonlinearity and the dispersiveness causing the solitary waves is studied in a relativistic plasma with negative ions through the derivation of a nonlinear partial-differential equation known as the Korteweg-de Vries equation. The negative ions play a salient part in the existence and behavior of the solitons and could be of interest in laboratory plasmas. First, the observations are made in a nonisothermal plasma, and later the reduction to the nonisothermality of the plasma shows entirely different characteristics as compared to the solitons in the isothermal plasmas. Comparison with the various solitons is emphasized     

尘埃等离子体中非线性波的叠加效应及稳定性问题

研究了小的有限振幅的无磁场尘埃等离子体中的非线性波.在一维情况下由Kortewegde Veries(KdV)方程来描述,考虑了二维情况下尘埃等离子体中尘埃颗粒上电荷的变化效应以及双温度离子效应后,尘埃等离子体受到横向高阶扰动后动力学方程由Kadomtsev-Petviashvili(KP)方程来描述.在此基础上,研究了以任意夹角传播的两个及三个孤立子的相互作用问题,考虑非线性效应后振幅相等的双孤立子在相互作用区域内振幅最大值是单个孤立子振幅的4倍,振幅相等的三孤立子在相互作用区域内振幅最大值是单个孤立子振幅的9倍.研究还表明波的传播方向受到横向高阶扰动后是稳定的.     

Spherical Kadomtsev-Petviashvili Solitons in a Suprathermal Complex Plasma

The nonlinear aspects of nonplanar dust acoustic (DA) solitary waves are investigated in an unmagnetized complex plasma comprising of cold dust grains,kappa-distributed ions as well as electrons.The nonplanar DA solitons are studied based on the reductive perturbation technique.It is shown that the evolution of DA solitons is governed by a spherical Kadomtsev-Petviashvili (sKP) equation and then the impact of suprathermality on the spatial structure as well as the nature of DA soliton is studied.It seems that the properties of DA solitons in nonplanar geometry are quite different from that of the planar solitons.     

Spherical Kadomtsev-Petviashvili Solitons in a Suprathermal Complex Plasma

The nonlinear aspects of nonplanar dust acoustic (DA) solitary waves are investigated in an unmagnetized complex plasma comprising of cold dust grains, kappa-distributed ions as well as electrons. The nonplanar DA solitons are studied based on the reductive perturbation technique. It is shown that the evolution of DA solitons is governed by a spherical Kadomtsev-Petviashvili (sKP) equation and then the impact of suprathermality on the spatial structure as well as the nature of DA soliton is studied. It seems that the properties of DA solitons in nonplanar geometry are quite different from that of the planar solitons.     

Low frequency electrostatic nonlinear structures in an inhomogeneous magnetized non-Maxwellian electron–positron–ion plasma

The properties of low frequency (coupled acoustic and drift wave) nonlinear structures including solitary waves and double layers in an inhomogeneous magnetized electron–positron–ion (EPI) nonthermal plasma with density and temperature inhomogeneities are studied in a simplified way. The nonlinear differential equation derived here for the study of double layers in the inhomogeneous EPI plasma resembles with the modified KdV equation in the stationary frame. But the method used for the derivation of nonlinear differential equation is simple and consistent to give both the stationary solitary waves and double layers. Further, the illustrations show that superthermality κ, drift velocity and temperature inhomogeneity have significant effects on the amplitude, width, and existence range of the structures.     

Algebraic Rossby Solitary Waves Excited by Non-Stationary External Source

The paper deals with the effects of non-stationary external source forcing and dissipation on algebraic Rossby solitary waves.From quasi-geostrophic potential vorticity equation,basing on the multiple-scale method,an inhomogeneous Korteweg-de Vries-Benjamin-Ono-Burgers(KdV-B-O-Burgers) equation is obtained.This equation has not been previously derived for Rossby waves.By analysis and calculation,four conservation laws associated with the above equation are first obtained.With the help of pseudo-spectral method,the waterfall plots are obtained and the evolutional characters of algebraic Rossby solitary waves are studied.The results show that non-stationary external source and dissipation have great effect on the generation and evolution of algebraic solitary Rossby waves.