Negative Solitons Research Articles

Ion acoustic solitons at the acoustic speed in a warm negative ion plasma with superthermal electrons

Using the Sagdeev pseudopotential method, the existence of Korteweg–de Vries (KdV) and non-KdV solitons is investigated in a negative ion plasma comprising adiabatic positive and negative ions and kappa distributed electrons. For some plasma parameter values, the plasma model supports the coexistence of solitons of both polarities. Positive KdV solitons coexist with negative non-KdV solitons at low values of negative to positive ion density ratio, and positive non-KdV solitons coexist with negative KdV solitons at higher values. There is therefore a switch in polarity between positive KdV and negative KdV solitons at a critical value of negative to positive ion density ratio and a switch in polarity between negative non-KdV and positive non-KdV solitons at the same point. At the critical point, there is no soliton at the acoustic speed, although there is coexistence at larger Mach numbers. This confirms that the existence of a soliton at acoustic speed is not a necessary condition for the coexistence of solitons of both polarities. When electrons are strongly non-thermal and the ion temperatures are important, the coexistence region vanishes and the non-KdV solitons disappear with it. It was also found that there is a forbidden region in terms of negative (positive) ion temperatures when the negative (positive) ion temperature increases with the other plasma parameters held fixed.

Arbitrary amplitude electron acoustic solitary excitations with Cairns–Tsallis distributed hot electrons and positrons in magnetized space plasmas

A rigorous theoretical study is performed to understand the characteristics of nonlinear electron acoustic (EA) solitary waves propagating in collisionless magnetized plasma system comprising cold inertial electrons, nonthermal–nonextensive hot electrons and positrons and stationary ions. The propagation and evolution of two potential modes (fast and slow) are studied in the linear regime. By employing magnetic hydrodynamic equations and with the aid of travelling wave approximation, the nonlinear wave dynamics is demonstrated by the first integral of motion in the form of a pseudo-energy balance equation. In exploring the EA soliton characteristics, numerical results reveal that only negative polarity EA solitons exist in a restricted range of the physical parametric space of the plasma system. It is revealed that the effects of nonthermal and nonextensive parameters, hot to cold electron density ratio, Mach number and magnetic strength considerably modify the basic properties of solitary waves. The present results may be important in space plasmas as well as laboratory plasmas with non-Maxwellian particle population.

Dust ion acoustic waves with Cairns–Tsallis electrons in the framework of KP-type equation

The features of dust ion acoustic waves (DIAWs) composed of cold ions, nonthermal nonextensive electrons as well as stationary dust particles are presented by KP-type equations. The effect of system parameters and higher order contributions on the phase velocity, amplitude and width of DIAWs is discussed. The parametric range for the existence of negative and positive solitons described by KP equation is presented. It is found that nonthermal and nonextensivity parameters and higher order contribution play a very crucial role in the formation of DIAWs. The results obtained would be valuable in interpreting certain nonlinear physical phenomena presented in the Earth's magnetosphere.

Dust ion acoustic solitons and double layers in a dusty plasma with adiabatic positive dust, adiabatic positive ion species, and Cairns-distributed electrons

The propagation of dust ion acoustic solitary waves and double layers is studied in a dusty plasma with heavy adiabatic positively charged dust grains and lighter adiabatic positive ions with Cairns-distributed electrons using the arbitrary amplitude Sagdeev pseudopotential approach. The analysis of the Sagdeev pseudopotential shows that this plasma model supports the propagation of positive solitons limited by the occurrence of the ion sonic point and negative solitons limited by the occurrence of double layers. Solitons of both polarities coexist for a range of some plasma parameters. We have shown that at a critical dust-to-ion density ratio, f, at which the third derivative of the Sagdeev pseudopotential vanishes, positive and negative solitons coexist without a soliton with finite amplitude at the acoustic speed, contrary to an earlier study. This suggests that the existence of a soliton with finite amplitude at the acoustic speed is not always a pre-requisite for the coexistence of nonlinear structures of both polarities. Positive and negative solitons coexist when the electrons are strongly nonthermal, with moderate ion thermal effects. Increasing ion thermal effect shifts the coexistence region to lower values of f, and when the ion thermal effects become important, negative solitons disappear and only positive solitons survive. The effects of different plasma parameters on the characteristics of the nonlinear structures have also been discussed in detail.

Arbitrary amplitude ion acoustic solitons, double layers and supersolitons in a collisionless magnetized plasma consisting of non-thermal and isothermal electrons

Abstract Using Sagdeev pseudo-potential technique, we have studied the arbitrary amplitude ion acoustic solitons, double layers and supersolitons in a collisionless plasma consisting of adiabatic warm ions, non-thermal hot electrons and isothermal cold electrons immersed in an external uniform static magnetic field. We have used the phase portraits of the dynamical system describing the non-linear behaviour of ion acoustic waves to confirm the existence of different solitary structures. We have found that the system supports (a) positive potential solitons, (b) negative potential solitons, (c) coexistence of both positive and negative potential solitons, (d) negative potential double layers, (e) negative potential supersolitons and (f) positive potential supersolitons. Again, we have seen that the amplitude of the positive potential solitons decreases or increases with increasing n ch according to whether 0 < n c h < n c h ( c ) $0{< }{n}_{ch}{< }{n}_{ch}^{\left(c\right)}$ or n c h ( c ) < n c h ≤ 1 ${n}_{ch}^{\left(c\right)}{< }{n}_{ch}\le 1$ , where n c h ${n}_{ch}$ is the ratio of isothermal cold and non-thermal hot electron number densities, and n c h ( c ) ${n}_{ch}^{\left(c\right)}$ is a critical value of n ch . Also, we have seen that the amplitude of the positive potential solitons decreases with increasing β e , where β e is the non-thermal parameter. We have also investigated the transition of different negative potential solitary structures: negative potential soliton (before the formation of negative potential double layer) → negative potential double layer → negative potential supersoliton → negative potential soliton (after the formation of negative potential double layer) by considering the variation of θ only, where θ is angle between the direction of the external uniform static magnetic field and the direction of propagation of the ion acoustic wave.

Nonlinear Propagation of Electrostatic Waves in Alkali–Fullerene Plasmas

Linear and nonlinear propagation of electrostatic waves is studied in electron-depleted bi-ion plasmas where positive and negative ions have different masses and charge states. The two-fluid model is used. The Korteweg–de Vries equation is obtained using the reductive perturbation technique. The results of the numerical calculations show that in K–fullerene plasma for the experimentally obtained temperature limits of both ions only a negative polarity soliton structure is obtained. Potential structures for some useful alkali–fullerene plasmas are also illustrated. Finally, the exact technique of the Sagdeev pseudopotential is used to consider arbitrary amplitude (large-amplitude) solitons in K–fullerene plasma.

Dust ion acoustic solitons in a complex dusty plasma system with an adiabatic state

In this theoretical work nonlinear behavior of dust ion acoustic solitary waves (SWs) has been investigated, and then the effect of the adiabatic change on them has been observed. The complex plasma system consists of inertial positive and negative ions, Maxwell's electrons, and positively and negatively charged stationary dust particles. The effects of dust polarity on the dust ion acoustic SWs have also been observed. Using the reductive perturbation method, we first derive K-dV equation which lets to analyze both the positive (bright) and negative (dark) solitons in a very limited region. After that mK-dV equation has been derived, and this let to analyze positive soliton for a large region, but cannot show the negative soliton. Finally, the Gardner equation has been derived employing the same method, through which we were able to analyze both the positive and negative solitons for a large region. It has been found that both the positive and negative solitons significantly depend on the mass number density, ion number density, and dust polarity in the adiabatic and isothermal system.

Planar and Nonplanar Solitons in Multi-Ion Dusty Plasma

A rigorous theoretical investigation has been made on nonlinear dust-ion-acoustic (DIA) solitary waves (SWs) in a multi-ion dusty plasma system, consisting of inertial positive and negative ions, and arbitrary charged stationary dust. The dust particles have been considered as arbitrarily (either positively or negatively) charged in order to observe the effects of dust polarity on the DIA SWs. Three different approaches (K-dV (Korteweg-de Vries), mK-dV (mixed K-dV), and Gardner) have been employed to analysis the entire regime. The reductive perturbation method has been employed in all these three approaches. Using reductive perturbation method, we first derive K-dV equation which let us to analyze both types (bright and dark) of solitons, but, in a very limited region. After that mK-dV equation has been derived which let us analyze bright soliton for a large region, but cannot show the dark soliton. Finally, we have derived the Gardner equation employing the same method, through which we were able to analyze both the bright and dark solitons for a large region. We also employed the modified Gardner (mG) equation to observe the effects of nonplanar geometry as well as time evolution of SWs. It has been found that both the positive and negative solitons depend on the ion number density of the ions, dust polarity, temperature, as well as time scale. It is also shown that the properties of the nonplanar (cylindrical and spherical) DIA-GSs are significantly different from those of the one dimensional planar ones.

Three-Dimensional Instability of Opposite Polarity Nonthermal Dusty Plasma

Abstract Nonlinearity properties of obliquely wave propagation and instability in collisionless magnetized nonthermal dusty plasmas containing fluid of negative-positive grains are investigated. Zakharov-Kuznetsov equation is obtained and the three-dimensional wave instability is studied. The parameters such as polarity charge ratio, cyclotron frequency and fast nonthermal effectiveness of the instability properties and growth rate are theoretically studied. It is found that both positive and negative soliton profiles are formed depending on the fraction ratio of electron-ion nonthermality. Also, the growth rate was dependent nonlinearly on the direction cosines, the cyclotron frequency and the positive (negative) grain charge ratio, but independent of the fractional ratio of electron-ion nonthermality. Present discussion may be very significant regarding the observations of nonlinear phenomena in space.

Effects of axial magnetic field and nonextensivity on small amplitude dust acoustic solitary waves in dusty plasma

The nonlinear propagation of small amplitude dust‐acoustic (DA) solitary waves in magnetized dusty plasma consisting of negatively charged mobile dust fluid, and Boltzmann‐distributed electrons and ions with two distinct temperatures following a q‐nonextensive distribution are investigated. In this article, a number of nonlinear equations, namely, the Korteweg–de‐Vries (K‐dV) equations, have been derived by employing the reductive perturbation technique that is valid for a small but finite amplitude limit. The effects of nonextensivity of ions with two distinct temperatures and dust concentration on the amplitude and width of DA solitary waves are investigated theoretically. It is observed that both the nonextensive and low‐temperatures ions significantly modify the basic properties and polarities of DA solitary waves. It is shown that both positive and negative potential DA solitons occur in this case. The implications of these results to some astrophysical environments and space plasmas (e.g., stellar polytropes, peculiar velocity distributions of galaxies, and collisionless thermal plasma), and laboratory dusty plasma systems are briefly mentioned.

Existence of electron acoustic solitary waves in relativistic limit

The nonlinear relativistic dynamics of electron acoustic waves (EAWs) in collisionless, unmagnetized plasma comprising cold inertial electrons, hot Boltzmann distributed electrons, and stationary ions are studied. The Sagdeev pseudopotential technique is employed to discuss the effect of equilibrium plasma species density and temperature of the hot electrons on the relativistic solitary wave solutions. In exploring the electron acoustic soliton characteristics, we encounter only negative polarity solitons which are found to exist in a restricted range of the physical parameter space of the system. In addition, we extend our analysis to demonstrate the wave breaking phenomena of EAW and estimate the maximum sustainable electric field amplitude of this mode considering the relativistic electron mass variation effect.

Heavy Ion-Acoustic Solitary Waves and Double Layers in a Multi-Ion Plasma

The formation and propagation of small-amplitude heavy-ion-acoustic (HIA) solitary waves and double layers in an unmagnetized collisionless multicomponent plasma system consisting of superthermal electrons, Boltzmann distributed light ions, and adiabatic positively charged inertial heavy ions are theoretically investigated. The reductive perturbation technique is employed to derive the modified Korteweg–de Vries (mKdV) and standard Gardner (SG) equations. The solitary wave (SW) solution of mKdV and SG equations, as well as double layers (DLs) solution of SG equation, is studied for analysis of higher order nonlinearity. It is found that the plasma system under consideration supports positive and negative potential Gardner solitons, but only positive potential mKdV solitons. In addition, it is shown that, the basic properties of HIA mKdV and Gardner solitons and DLs (viz. polarity, amplitude, width, and phase speed) are incomparably influenced by the adiabaticity effect of heavy ions and the superthermality effect of electrons. The relevance of the present findings to the system of space plasmas, as well as to the system of researchers interest, is specified.

Weakly dissipative dust acoustic solitons in the presence of superthermal particles

An investigation of the linear and non‐linear properties of low‐frequency electrostatic (dust acoustic) waves in a collisional dusty plasma with negative dust grains, Maxwellian electrons, and κ‐distributed ions is carried out. Low dust–neutral collisions accounting for dissipation (wave damping effect) is considered. The linear properties of dust acoustic excitations are discussed for varying values of relevant plasma parameters. It is shown that large wavelengths (beyond a critical value) are overdamped. In the limit of low dust–neutral collision rate, we have derived a damped Korteweg de Vries (KdV) equation by using the reductive perturbation technique. Supplemented by vanishing boundary conditions, the time‐varying solution of damped KdV equation leads to a weakly dissipative negative potential soliton. The soliton evolution with the damping parameter and other physical plasma parameters (superthermality, dust concentration, ion temperature) is delineated.

Oblique propagation of solitary electrostatic waves in magnetized plasmas with cold ions and nonthermal electrons

Oblique propagation of large amplitude electrostatic waves and solitary structures is investigated in magnetized plasmas, comprising cold fluid ions and Cairns nonthermally distributed electrons, by using a Sagdeev pseudopotential formalism. To perform the analysis, quasineutrality is assumed, so that in normalized variables the electrostatic potential and the occurrence of solitary structures are governed by three parameters: the Mach number M, the typical Cairns parameter β, and the angle ϑ between the directions of propagation and the static magnetic field. Below a critical β, only positive compressive solitons are possible, and their amplitudes increase with increasing β, M, and ϑ. Above the critical β, there is coexistence between negative rarefactive and positive compressive solitons, and the range of negative solitons, at increasing M, ends upon encountering a double layer or a singularity. The double layer amplitudes (in absolute value) increase with β but are independent of ϑ. Roots of the Sagdeev pseudopotential beyond the double layer are not accessible from the undisturbed conditions, because of an intervening singularity where the pseudopotential becomes infinite. Recent claims of finding supersolitons beyond a double layer appear to be based on a misinterpretation of the nature of the singularity.

Zakharov Kuznetsov equation for four component dust magnetoplasma using the multi-fluid concept

The present article aims to put forward a theoretical and numerical investigation of linear and nonlinear dust ion acoustic (DIA) waves in a four component magnetized dusty plasma by using the multi-fluid concept. In particular the dynamics of low amplitude DIA solitons is investigated via the Zakharov Kuznetsov type nonlinear evolution equation derived by employing the reductive perturbation technique. We consider two cases. The first one considers the existence and propagation of DIA waves in a four component dusty plasma when the ions are inertial while the dust particulates are assumed to be stationary, while in the second case the ions and both positively and negatively charged dust grains are assumed as inertial species. Electrons in both cases are considered to be isothermal. It is observed that both the positive and negative solitons are coexisted in the present plasma model. The characteristics of DIA solitons in both cases are investigated with effect of the both positive and negative dust concentrations, magnetic field and different temperature ratios. By using the small-k expansion method the soliton stability analysis is carried out for both cases. It appears timely to add that the theoretical results presented herein are supported by the numerical analysis and illustrations. The relevance of the study carried out to the laboratory and cosmic plasmas is also pointed out.

A small-amplitude study of solitons near critical plasma compositions

The properties of small-amplitude solitons are established near critical plasma compositions in a generalized fluid plasma with an arbitrary number of species. The study is conducted via a Taylor series expansion of the Sagdeev potential. It is shown that there are two types of critical compositions, namely rich critical and poor critical compositions. The coexistence of positive and negative polarity solitons is shown to arise at rich critical compositions and near rich critical compositions. At poor critical compositions, no small-amplitude solitons exist, while weak double layers arise near poor critical compositions. A novel analytical expression is obtained for a small-amplitude acoustic speed soliton solution near rich critical compositions. These solitons have a Lorentzian shape with much fatter tails than regular solitons. A case study is also performed for a simple fluid model consisting of cold ions and two Boltzmann electron species. Exact agreement is obtained between the Sagdeev analysis and reductive perturbation theory. For the first time, we derive the same Lorentzian acoustic speed soliton from reductive perturbation theory.

Nonlinear dynamics of soliton collisions in electronegative plasmas: The phase shifts of the planar KdV- and mkdV-soliton collisions

The collisions of weakly nonlinear structures in an electronegative plasma consisting of Boltzmann electrons, Boltzmann negative ions, and cold mobile positive ions are investigated depending on experimental data. Our attention is focused on the study of the face-to-face soliton collisions, i.e. head-on soliton collisions. To do this, the extended Poincaré–Lighthill–Kuo (PLK) reductive perturbation method is used. The present study is split into two parts: the first one, called generic case. In this case, the two-coupled Korteweg–de Vries (KdV) equations and the analytical phase shifts after the head-on collision of the two-KdV solitons are obtained. Our numerical calculations, showed that both compressive and rarefactive solitons can exist in such plasma, depending on the relevant physical plasma parameters, namely the electrons-to-negative ion temperature ratio and the negative ion concentration. It is found that the phase shift has a positive sign for compressive solitary structures and negative sign for rarefactive solitary structures. At the critical value of the temperature ratio, the two-coupled modified Kortwege–de Vries (mKdV) equations are used to study the soliton collision rather than the two-KdV equations and the analytical phase shifts after the collision are derived. In the latter case (called special case), the combinations of negative and positive soliton collision can occur, contrary to the generic case, where both soliton collisions necessarily have the same polarity. The plasma parameter values for laboratory experiment are taken for discussion.

Anomalous waves in gas-liquid mixtures near gas critical point in Gardner equation approximation

The waves in a bubbled incompressible liquid with Van der Waals gas in a bubbles being near critical points is considered in a frame of Gardner equation. It is shown that both coefficients on quadratic and cubic nonlinear terms in Gardner equation change the sign near gas critical point and it results the anomalous waves: negative and limited solitons, kinks, antikinks and breathers. The dynamics and interactions of these waves was studied numerically by high accuracy Fourier methods with periodically boundary conditions. In particular it is revealed that limited solitons always arise from initial distribution with a few identical soliton's pair and stand stable in their form after numerous interactions.

Soliton dynamics to the multi-component complex coupled integrable dispersionless equation

The generalized coupled integrable dispersionless (CID) equation describes the current-fed string in a certain external magnetic field. In this paper, we propose a multi-component complex CID equation. The integrability of the multi-component complex equation is confirmed by constructing Lax pairs. One-soliton and two-soliton solutions are investigated to exhibit rich evolution properties. Especially, similar as the multi-component short pulse equation and the first negative AKNS equation, periodic interaction, parallel solitons, elastic and inelastic interaction, energy re-distribution happen between two solitons. Multi-soliton solutions are given in terms of Pfaffian expression by virtue of Hirota’s bilinear method.

Generation of Weak Double Layers and Low-Frequency Electrostatic Waves in the Solar Wind

We propose that the mechanism for the generation of weak double layers (WDLs) and low-frequency coherent electrostatic waves, observed by Wind in the solar wind at 1 AU, might be slow and fast ion-acoustic solitons and double layers. The solar wind plasma is modelled as a fluid of hot protons and hot $\alpha$ particles streaming with respect to protons, and suprathermal electrons having a $\kappa$ -distribution. The fast ion-acoustic mode is similar to the ion-acoustic mode of a proton–electron plasma and can support only positive-potential solitons. The slow ion-acoustic mode is a new mode that occurs due to the presence of $\alpha$ particles. This mode can support both positive and negative solitons and double layers. The slow ion-acoustic mode can exist even when the relative streaming, $U_{0}$ , between $\alpha$ particles and protons is zero, provided that the $\alpha$ temperature, $T_{i}$ , is not exactly equal to four times the proton temperature, $T_{p}$ . An increase of the $\kappa$ -index leads to an increase in the critical Mach number, maximum Mach number, and the maximum amplitude of both slow and fast ion-acoustic solitons. The slow ion-acoustic double layer can explain the amplitudes and widths, but not the shapes, of the observed WDLs in the solar wind at 1 AU by Wind spacecraft. The Fourier transform of the slow ion-acoustic solitons/double layers would produce broadband low-frequency electrostatic waves having main peaks between 0.35 kHz to 1.6 kHz, with an electric field in the range of $E = (0.01\,\mbox{--}\,0.7)~\mbox{mV}\,\mbox{m}^{-1}$ , in excellent agreement with the observed low-frequency electrostatic wave activity in the solar wind at 1 AU.