Negative Solitons Research Articles

Ion-acoustic solitons, double layers and supersolitons in a plasma with two ion- and two electron species

The polarity of ion-acoustic solitons that arise in a plasma with two (same mass, different temperature) ion species and two (different temperature) electron species is investigated. Two different fluid models are compared. The first model treats all species as adiabatic fluids, while the second model treats the ion species as adiabatic, and the electron species as isothermal. Nonlinear structures are analysed via the reductive perturbation analysis and pseudo-potential analysis. Each model supports both slow and fast ion-acoustic solitons, associated with the two (slow and fast) ion-acoustic speeds. The models support both positive and negative polarity solitons associated with the slow ion-acoustic speed. Moreover, results are in good agreement, and both models support positive and negative polarity double layers. For the fast ion-acoustic speed, the first model supports only positive polarity solitons, while the second model supports solitons of both polarity, coexistence of positive and negative polarity solitons, double layers and supersolitons. A novel feature of our analysis is the evaluation of nonlinear structures at critical number densities where polarity changes occur. This analysis shows that solitons that occur at the acoustic speed are neither a necessary nor a sufficient condition for the phenomenon of coexistence. The relationship between the existence regions of supersolitons and soliton polarity is also discussed.

Surface defect gap solitons in superlattices with self-defocusing nonlinearity

We put forward the existence and stability of defect surface gap solitons at the interface between uniform media and an superlattice with self-defocusing nonlinearity. We reveal that the defect plays the significant role in controlling the region of solitons existing. Various solitons are found to be existed in different gaps for different defects. For positive defects, fundamental solitons can exist stably in the semi-infinite gap, and dipole solitons can exist stably in the first gap but they are unstable in the second gap. For zero or negative defects, fundamental and dipole solitons can exist stably in the first gap and the second gap, respectively.

Nonlinear structures of the Korteweg-de Vries and modified Korteweg-de Vries equations in non-Maxwellian electron-positron-ion plasma: Solitons collision and rogue waves

Solitons (small-amplitude long-lived waves) collision and rogue waves (large-amplitude short-lived waves) in non-Maxwellian electron-positron-ion plasma have been investigated. For the solitons collision, the extended Poincaré-Lighthill-Kuo perturbation method is used to derive the coupled Korteweg-de Vries (KdV) equations with the quadratic nonlinearities and their corresponding phase shifts. The calculations reveal that both positive and negative polarity solitons can propagate in the present model. At critical value of plasma parameters, the coefficients of the quadratic nonlinearities disappear. Therefore, the coupled modified KdV (mKdV) equations with cubic nonlinearities and their corresponding phase shifts have been derived. The effects of the electron-to-positron temperature ratio, the ion-to-electron temperature ratio, the positron-to-ion concentration, and the nonextensive parameter on the colliding solitons profiles and their corresponding phase shifts are examined. Moreover, generation of ion-acoustic rogue waves from small-amplitude initial perturbations in plasmas is studied in the framework of the mKdV equation. The properties of the ion-acoustic rogue waves are examined within a nonlinear Schrödinger equation (NLSE) that has been derived from the mKdV equation. The dependence of the rogue wave profile on the relevant physical parameters has been investigated. Furthermore, it is found that the NLSE that has been derived from the KdV equation cannot support the propagation of rogue waves.

Nonplanar solitons collision in ultracold neutral plasmas

Collisions between two nonplanar ion-acoustic solitons in strongly coupled ultracold neutral plasmas composed of ion fluid and non-Maxwellian (nonthermal or superthermal) electron distributions are investigated. The extended Poincare-Lighthill-Kuo method is used to obtain coupled nonplanar Kortweg-de Vries equations for describing the system. The nonplanar phase shifts after the interaction of the two solitons are calculated. It is found that the properties of the nonplanar colliding solitons and its corresponding phase shifts are different from those in the planar case. The polarity of the colliding solitons strongly depends on the type of the non-Maxwellian electron distributions. A critical nonthermality parameter βc is identified. For values of β ≤ βc solitons with double polarity exist, while this behavior cannot occur for superthermal plasmas. The phase shift for nonthermal plasmas increases below βc for a positive soliton, but it decreases for β > βc for a negative soliton. For superthermal plasmas, the phase shift enhances rapidly for low values of spectral index κ and higher values of ions effective temperature ratio σ*. For 2 ≲ κ<10, the phase shift decreases but does not change for κ > 10. The nonlinear structure, as reported here, is useful for controlling the solitons created in forthcoming ultracold neutral plasma experiments.

Surface lattice solitons in saturable nonlinear media driven by the quadratic electro-optic effect

We study theoretically surface lattice solitons driven by quadratic electro-optic effect at the interface between uniform media and an optical lattice with or without a defect. The surface defect of optical lattice strongly affects the surface soliton properties. Surface solitons originating from a positive defect can be formed in the semi-infinite and first bandgap, negative surface solitons exist in finite bandgap but are absent in the semi-infinite bandgap. These solitons associated with different bandgaps possess different stability properties. It is also shown that, as the propagation constant increases, these positive surface solitons can laterally drift toward the optical lattice and the uniform medium in the semi-infinite and first bandgap, respectively. Moreover, for a better comparison, the surface solitons and their stability at the interface between uniform media and a uniform photonic lattice are also examined in detail.

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.

Higher order nonlinear equations for the dust-acoustic waves in a dusty plasma with two temperature-ions and nonextensive electrons

The nonlinear propagation of dust-acoustic waves in a dusty plasma whose constituents are negatively charged dust, Maxwellian ions with two distinct temperatures, and electrons following q-nonextensive distribution, is investigated by deriving a number of nonlinear equations, namely, the Korteweg-de-Vries (K-dV), the modified Korteweg-de-Vries (mK-dV), and the Gardner equations. The basic characteristics of the hump (positive potential) and dip (negative potential) shaped dust-acoustic (DA) Gardner solitons are found to exist beyond the K-dV limit. The effects of two temperature ions and electron nonextensivity on the basic features of DA K-dV, mK-dV, and Gardner solitons are also examined. It has been observed that the DA Gardner solitons exhibit negative (positive) solitons for q<qc (q>qc) (where qc is the critical value of the nonextensive parameter q). The implications of our results in understanding the localized nonlinear electrostatic perturbations existing in stellar polytropes, quark-gluon plasma, protoneutron stars, etc. (where ions with different temperatures and nonextensive electrons exist) are also briefly addressed.

Highlights from the Asia Pacific Region

It is well known that multicomponent plasma with negative ions supports a number of wave modes such as ion-acoustic solitons described by the Kortewege-de Vries (KdV) equation, modified KdV solitons at critical density of negative ions and ion-acoustic envelop solitons described by nonlinear Schrödinger equation (NLSE). The NLSE which is equivalent to the mKdV equation is applicable in describing evolution of ion-acoustic wave in plasma at critical density of negative ions which becomes modulationaly unstable when the nonlinear co-efficient is negative.

Characteristics of ion acoustic solitary waves in a negative ion plasma with superthermal electrons

The behavior of ion acoustic solitons in a plasma including positive and negative ions and kappa distributed electrons is studied, using both small amplitude and arbitrary amplitude approaches. The existence regions of compressive and rarefactive solitons will depend on negative to positive ion density ratio (ν) and kappa parameter as well as positive to negative ion mass ratio (Q). The numerical analysis of Sagdeev potential shows that for a chosen plasma with fixed Q, the existence regime of compressive solitons is decreased (increased) by increasing density ratio (kappa parameter), while for rarefactive solitons these conditions are quite opposite. Additionally, the possibility of propagation of both compressive and rarefactive subsonic solitons is investigated. It is found that by increasing negative ions, the existence domains of subsonic solitons are decreased, so that in excess of negative ions subsonic solitons will not propagate even at the presence of superthermal electrons. Indeed, there is a critical negative ion density ratio for all values of kappa, above that only supersonic solitons are observed. Furthermore, in addition to the previous results based on Cairns-distributed electrons [R. A. Cairns et al., Geophys. Res. Lett. 22, 2709 (1995)], which predicted that both compressive and rarefactive solitons can coexist simultaneously, we have also found the regions of ν and κ in which either positive or negative potentials are permitted (i.e., not together). This research will be helpful in understanding the properties of space and laboratory plasmas containing negative ions with energetic electrons.

Evolution of higher order nonlinear equation for the dust ion-acoustic waves in nonextensive plasma

There are three different types of nonlinear equations, namely, Korteweg-de Vries (K-dV), modified K-dV (mK-dV), and mixed modified K-dV (mixed mK-dV) equations, for the nonlinear propagation of the dust ion-acoustic (DIA) waves. The effects of electron nonextensivity on DIA solitary waves propagating in a dusty plasma (containing negatively charged stationary dust, inertial ions, and nonextensive q distributed electrons) are examined by solving these nonlinear equations. The basic features of mixed mK-dV (higher order nonlinear equation) solitons are found to exist beyond the K-dV limit. The properties of mK-dV solitons are compared with those of mixed mK-dV solitons. It is found that both positive and negative solitons are obtained depending on the q (nonextensive parameter).

Head-on collisions of electrostatic solitons in nonthermal plasmas

In contrast to overtaking interactions, head-on collisions between two electrostatic solitons can be dealt with only by use of an approximate method, which limits the range of validity but offers valuable insights. Treatments in the plasma physics literature all use assumptions in the stretching of space and time and in the expansion of the dependent variables that are seldom, if ever, discussed. All models force a separability to lowest order, corresponding to two linear waves with opposite but equally large velocities. A systematic exposition of the underlying hypotheses is illustrated by considering a plasma composed of cold ions and nonthermal electrons. This is general enough to yield critical compositions that lead to modified rather than standard Korteweg-de Vries equations, an aspect not discussed so far. The nonlinear evolution equations for both solitons and their phase shifts due to the collision are established. A Korteweg-de Vries description is the generic conclusion, except when the plasma composition is critical, rendering the nonlinearity in the evolution equations cubic, with concomitant repercussions on the phase shifts. In the latter case, the solitons can have either polarity, so combinations of negative and positive solitons can occur, contrary to the generic case, where both solitons necessarily have the same polarity.

Head-on collisions of electrostatic solitons in multi-ion plasmas

Head-on collisions between two electrostatic solitons are dealt with by the Poincaré-Lighthill-Kuo method of strained coordinates, for a plasma composed of a number of cold (positive and negative) ion species and Boltzmann electrons. The nonlinear evolution equations for both solitons and their phase shift due to the collision, resulting in time delays, are established. A Korteweg-de Vries description is the generic conclusion, except when the plasma composition is special enough to replace the quadratic by a cubic nonlinearity in the evolution equations, with concomitant repercussions on the phase shifts. Applications include different two-ion plasmas, showing positive or negative polarity solitons in the generic case. At critical composition, a combination of a positive and a negative polarity soliton is possible.

Arbitrary amplitude ion-acoustic soliton coexistence and polarity in a plasma with two ion species

Using a Sagdeev pseudopotential formalism, large ion-acoustic waves are investigated in a multispecies plasma model consisting of two cold positive ion species in the presence of nonthermal Cairns electrons. Positive solitons are limited in amplitude by infinite compression of the lighter ion species. Negative solitons become possible at a sufficient degree of electron nonthermality, and their amplitudes are limited by the occurrence of double layers. What determines coexistence is the possibility of having parameter ranges for which there are solitons at the acoustic speed, which is a necessary and sufficient condition but unfortunately not an easy criterion to check analytically. For the first time a parameter range has been found where both negative and positive polarity solutions coexist, with the solitons at the acoustic speed always having a positive polarity, contrary to earlier results which seemed to indicate that polarity switches and coexistence ranges were linked. Finally, some useful proofs are presented in an Appendix, concerning the Sagdeev pseudopotential behavior at the acoustic speed, results of which are generic to a range of physical plasma models.

Dust-acoustic solitary modes in plasmas with isothermal and nonthermal ions: Polarity switches and coexistence domains

Large dust-acoustic waves are investigated in a multispecies plasma model consisting of cold negative dust in the presence of cooler Boltzmann and hotter nonthermal Cairns positive ions, in a Sagdeev pseudopotential formalism. Use of the pseudopotential at the acoustic speed itself yields in a systematic way compositional parameter values where negative/positive solitons interchange polarities and also where both polarities coexist. The latter requires that solitons at the acoustic speed exist, with finite amplitudes, compared to superacoustic solitons of the opposite polarity. The coexistence region starts when the pseudopotential at the acoustic speed has a negative root at the limit of infinite dust compression and ends when a positive double root is encountered. Outside the coexistence domain, only negative or positive superacoustic solitons can exist. Thus, the discussion and numerical evaluations are guided by precise physical and analytic arguments rather than mere numerical experimentation. Graphs of relevant Sagdeev pseudopotentials illustrate the link with the analytical constraints.

Ion acoustic solitary waves in an electron–positron–ion plasma with non-thermal electrons

Using the Sagdeev potential approach, arbitrary amplitude modified ion acoustic solitons and double layers have been studied in an electron–positron–ion (e–p–i) plasma composed of Cairns-distributed electrons, Boltzmann positrons and cold ions. Existence domains are presented in different slices of parameter space, and care is taken to differentiate between behaviour at a fixed soliton speed, and at the Mach number normalized with respect to the true acoustic speed for the three-component plasma. Negative solitons, limited in Mach number by double layers, have been found over small ranges in β, relative positron density and Mach number. These have not previously been reported in an e–p–i plasma. A region of ‘coexistence’ in parameter space has been identified, in which solitons of both polarities are supported. In this region, one polarity behaves in a ‘Korteweg–de Vries (KdV)-like’ fashion, vanishing at the acoustic speed, while solitons of the other polarity have finite amplitude at the acoustic speed (‘non-KdV-like’), as has been reported recently in a number of other plasma models. This work extends considerably and also corrects some errors in a recent publication (Pakzad 2009 Phys. Lett. A 373 847–50).

A new conduction phenomenon observed in polyethylene and epoxy resin: Ultra‐fast soliton conduction

AbstractA new conduction mechanism in polyethylene and epoxy resin is presented and discussed in this article. This mechanism is based on the presence of charge pulses that can be seen as solitons (solitary waves) crossing dielectrics with mobility 4–5 orders of magnitude larger than that of conventional charge carriers. The nature of this new process that is characterized by charge pulses with such high mobility requires a completely different mechanism for transport to be theorized with respect to that, mediated by trap sites, of conventional charge carriers. It is speculated in this article that injection and transport of positive and negative solitons occurs through the coupling of space charge and relaxation processes involving molecular chains, but of different nature for negative or positive solitons. Observation of space charge shows the existence of such solitons for at least two families of materials, polyethylene, and epoxy resin. In addition, it has been observed that nanostructuration, which is able to modify mechanical properties, affects also the presence and size of the solitons. In this article, we not only seek to demonstrate the existence of this new phenomenon, but attempt to provide an explanation and a kind of qualitative–quantitative model, which shows that the assumption of a pulsive conduction mechanism mediated by chain relaxation processes, transport in free volume (for negative solitons), and reverse‐tunneling between macromolecular chains (positive solitons) seems to fit quite well with the experimental observations. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011

Propagation of ion-acoustic waves in a warm dusty plasma with electron inertia

The KdV equation is derived for weakly nonlinear ion-acoustic waves in an unmagnetized warm dusty plasma with electron inertia. It has been shown that the inclusion of electron inertia and pressure variation of the species not only significantly modifies the basic features (width and amplitude) of dust ion-acoustic solitions, but also introduces a new parametric regime for the existence of positive and negative solitons.

Ion- and electron-acoustic solitons and double layers in multi-component space plasmas

A general model for the ion- and electron-acoustic solitons and double layers in a multi-component unmagnetized plasma consisting of background electrons, counter-streaming electron beams and ions is discussed. The model is based on the multi-fluid equations and the Poisson equation, and uses the Sagdeev pseudo-potential techniques. For identical counter-streaming electron beams and depending upon the plasma parameters, three types of solutions, namely, ion-acoustic, slow and fast electron-acoustic soliton/double layer, are possible. Generally, the ion acoustic solitons have positive potentials, slow-electron acoustic solitons have negative potentials and fast electron-acoustic solitons and double layers can have either positive or negative potentials depending on the core electron density. As beam speed is increased, first ion-acoustic and then slow electron-acoustic solitons disappear. At large beam speed, only fast electron-acoustic solitons/double layers survive. The results may be relevant to the observations of the electrostatic solitary waves (ESWs) observed in the Earth’s magnetosphere.

Nonthermal effects on existence domains for dust-acoustic solitary structures in plasmas with two-temperature ions

Large dust-acoustic waves are investigated in a multispecies plasma model consisting of adiabatic, negatively charged dust, in the presence of two ion species, a cooler one with a Boltzmann distribution and a hotter one with a nonthermal Cairns distribution. This is treated through a Sagdeev pseudopotential analysis, in a way which is physically transparent and puts great emphasis on the existence domains in compositional parameter space. The occurrence and properties of positive double layers have been studied, and this automatically also includes the existence domains for positive solitons with velocities and amplitudes smaller than the double layer values. A brief discussion is given of negative solitons and of conditions affecting the coexistence of negative and positive solitary structures for the same plasma properties. Subject to simple adjustments, these results apply equally to the conjugate plasma model of positive dust and two electron species, and in the limit without nonthermal effects, to the case of ion-acoustic solitary structures in a plasma with double Boltzmann electrons, and extensions of earlier results of that problem are presented.

Solitons in dusty plasmas with positive dust grains

Although “typical” micrometer-sized dust grains in a space or laboratory plasma are often negatively charged because of collisions with the mobile electrons, there are environments in which grains may take on a positive charge. We consider a dusty plasma composed of electrons, positive ions and positive dust grains, and use the fluid dynamic paradigm to identify existence domains in parameter space for both dust-acoustic (DA) and dust-modified ion-acoustic (DIA) solitons. Only positive potential DA solitons are found. This represents an expected antisymmetry with the case of negative dust, where previously only negative solitons were reported. However, whereas for negative dust DIA solitons of either sign of potential may exist, we find that for the case of positive dust, DIA solitons are restricted to positive potentials only. The results for both positive and negative dust are consistent with an hypothesis that, in the absence of flows, the sign(s) of the soliton potential coincide(s) with the sign(s) of the species whose inertia is included in the calculation; i.e., the cold, supersonic species present in the plasma.