Solitary Wave Structures Research Articles

Spatial Evolution of Electrostatic Solitary Waves along Plasma Sheet Boundary Layer Adjacent to the Magnetic Reconnection X-Line

Analysis on the spatial structure of electrostatic solitary waves (ESWs) along the plasma sheet boundary layer (PSBL) near an on-going magnetic reconnection X-line is performed. Most of the ESWs in the PSBL of R3 region near reconnection X-line are propagating earthwards away from the reconnecting site. An analysis of their spatial structure shows that, when ESWs propagate along the ambient field in the PSBL, outwards from the magnetic reconnection X-line, their amplitude will finally attenuate and thus the electron hole will fade away but their spatial scale remains unchanged. However, the spatial structure of propagating ESWs evolves from 1-D-like to 2-D-like though totally in a 1-D structure.

The Effect of Spectral Index Parameter κ on Obliquely Propagating Solitary Wave Structures in Magneto-Rotating Plasmas

Nonlinear ion-acoustic solitary wave structures in collisionless, non-relativistic, homogenous, magneto-rotating plasma, in which the electron species follow the kappa distribution function, are studied. The Korteweg-de Vries (KdV) equation is derived by using the reductive perturbation method, and the effects of different plasma parameters on the obliquely propagating nonlinear solitary wave structures in the magneto-rotating plasma are presented. It is noticed that the spectral index parameter κ significantly modifies the nonlinear wave structure.

(3 + 1)-dimensional cylindrical Korteweg-de Vries equation for nonextensive dust acoustic waves: Symbolic computation and exact solutions

By combining the effects of bounded cylindrical geometry, azimuthal and axial perturbations, the nonlinear dust acoustic waves (DAWs) in an unmagnetized plasma consisting of negatively charged dust grains, nonextensive ions, and nonextensive electrons are studied in this paper. Using the reductive perturbation method, a (3 + 1)-dimensional variable-coefficient cylindrical Korteweg-de Vries (KdV) equation describing the nonlinear propagation of DAWs is derived. Via the homogeneous balance principle, improved F-expansion technique and symbolic computation, the exact traveling and solitary wave solutions of the KdV equation are presented in terms of Jacobi elliptic functions. Moreover, the effects of the plasma parameters on the solitary wave structures are discussed in detail. The obtained results could help in providing a good fit between theoretical analysis and real applications in space physics and future laboratory plasma experiments where long-range interactions are present.

Analytical study on the existence of ion-acoustic solitary waves in a plasma consisting of warm streaming ions and nonthermal electrons

Theoretical investigations have been made for the formation of ion-acoustic solitary wave structure in a plasma consisting of warm streaming positive ions and nonthermal electrons. Analytical solutions have been obtained with some sufficient and necessary conditions for the existence of ion-acoustic solitary waves. Some critical values of the ion temperature and the nonthermal parameter of electrons have been obtained and presented graphically. It is shown that drift of the ions and the nonthermal electrons have significant effects on the formation of ion-acoustic solitary waves. In presence of the streaming motion of the ions, two distinct modes (fast and slow) of propagation have been obtained. Limiting values of the soliton speed for these modes have been calculated. It is found that the drift motion and ion temperature change significantly the conditions for the existence and properties of ion-acoustic solitons.

Solitons and Gibbs Measures for Nonlinear Schrödinger Equations

We review some recent results concerning Gibbs measures for nonlinear Schrödinger equations (NLS), with implications for the theory of the NLS, including stability and typicality of solitary wave structures. In particular, we discuss the Gibbs measures of the discrete NLS in three dimensions, where there is a striking phase transition to soliton-like behavior.

Ion acoustic solitons in negative ion plasmas with superthermal electrons

Korteweg-de Vries (KdV) equation for electrostatic wave in an unmagnetized negative ion plasma with superthermal electrons is derived using reductive perturbation technique. A generalized Lorentzian distribution (kappa distribution) is assumed for the electrons. The influence of spectral index (kappa) on the soliton is discussed in the presence of the negative ions. It is found that different plasma parameters such as (negative ion temperature, positive ion temperature, negative ion concentration, mass ratio of positive to negative ion) in the presence of superthermal electrons modify the ion acoustic solitary wave structure significantly.

Nonlinear structure of ion-acoustic solitary waves in a relativistic degenerate electron–positron–ion plasma

AbstractArbitrary amplitude and small amplitude ion-acoustic solitary waves (IASWs) have been investigated in a relativistic, collisionless, unmagnetized, and degenerate dense electron–positron–ion plasma. The arbitrary amplitude IASWs have been studied by using the Sagdeev-type pseudo-potential approach. Along with approximate solution, the exact amplitude solitary structure has also been studied numerically. The electrons and positrons are assumed to follow the corresponding Fermi distribution function and the ions are described by the hydrodynamic equations. A new dispersion relation for the ion-acoustic wave has been derived for the relativistic Thomas–Fermi plasma. An energy balance-like equation involving the Sagdeev-type pseudo-potential has been investigated and it has been shown that the concentration of plasma particles has significant effect on the permitted Mach number range of IASWs. Also, it has been pointed out that the only compressional supersonic IASWs can propagate in the relativistic Thomas–Fermi plasma. The present work would be helpful to understand the excitation of the nonlinear ion-acoustic waves in a degenerate plasma, such as in superdense white dwarfs and in the cores of massive planets.

Trapping effects in a self-gravitating quantum dusty plasma

The effects of trapping on the nonlinear properties of dust-acoustic waves in an unmagnitized collisionless self-gravitating plasma were studied by treating the ions to be Maxwellian, the dust to be cold and the electrons to be degenerate. The effect of trapping and the gravitational potential on the nonlinear structures was investigated by employing the Sagdeev potential approach, which shows that the features of solitary wave structures are affected by changes in Mach number as well as ion temperature and other physical parameters of the system. Modulational stability analysis is also presented, and the regions of stability and instability are discussed.

A nonlinear Zakharov-Kuznetsov equation in magnetized plasma with q-nonextensive electrons velocity distribution

By using the reductive perturbation method (RPM), a nonlinear Zakharov-Kuznetsov (ZK) equation for ion-acoustic solitary waves (IASWs) is derived for a magnetized plasma in which the electrons are nonextensively distributed. The combined effects of electron nonextensivity, strength of magnetic field, and obliqueness on the ion acoustic (IA) solitary profile are analyzed. Three different ranges of the nonextensive q-parameter are considered. It is observed that the system may support both compressive as well as rarefactive solitons. The magnetic field has no effect on the amplitude of solitary waves whereas the obliqueness affects both the amplitude as well as the width of the solitary wave structures.

Nonlinear waves and coherent structures in the quantum single-wave model

Starting from the von Neumann-Maxwell equations for the Wigner quasi-probability distribution and for the self-consistent electric field, the quantum analog of the classical single-wave model has been derived. The linear stability of the quantum single-wave model has been studied, and periodic in time patterns have been found both analytically and numerically. In addition, some features of quantum chaos have been detected in the unstable region in parameter space. Further, a class of standing-wave solutions of the quantum single-wave model has also been found, which have been observed to behave as stable solitary-wave structures. The analytical results have been finally compared to the exact system dynamics obtained by solving the corresponding equations in Schrodinger representation numerically.

On the structure and propagation of internal solitary waves generated at the Mascarene Plateau in the Indian Ocean

Analysis of a comprehensive dataset of Synthetic Aperture Radar (SAR) images acquired over the sea area around the Mascarene Plateau in the western Indian Ocean reveals, for the first time, the full two-dimensional spatial structure of internal solitary waves in this region of the ocean. The satellite SAR images show that powerful internal waves radiate both to the west and east from a central sill near 12.5°S, 61°E between the Saya de Malha and Nazareth Banks. To first order, the waves appear in tidally generated packets on both sides of the sill, and those on the western side have crest lengths in excess of 350 km, amongst the longest yet recorded anywhere in the world's oceans. The propagation characteristics of these internal waves are well described by first mode linear waves interacting with background shear taken from the westward-flowing South Equatorial Current (SEC), a large part of which flows through the sill in question. Analysis of the timings and locations of the packets indicates that both the westward- and eastward-traveling waves are generated from the western side of the sill at the predicted time of maximum tidal flow to the west. The linear generation mechanism is therefore proposed as the splitting of a large lee wave that forms on the western side of the sill, in a similar manner to that already identified for the shelf break generation of internal waves in the northern Bay of Biscay. While lee waves should form on either side of the sill in an oscillatory tidal flow, that on the western side would be expected to be much larger than that on the eastern side because of a superposition of the tidal flow and the steady westward flow of SEC. The existence of a large lee wave at the right time in the tidal cycle is then finally confirmed by direct observations. Our study also confirms the existence of second mode internal waves that form on the western side of the sill and travel across the sill towards the east.

Nonlinear Korteweg–de Vries equation for soliton propagation in relativistic electron-positron-ion plasma with thermal ions

The nonlinear propagation of ion-acoustic solitons in relativistic electron-positron-ion plasma comprising of Boltzmannian electrons, positrons, and relativistic thermal ions has been examined. The Korteweg–de Vries equation has been derived by reductive perturbation technique. The effect of various plasma parameters on amplitude and structure of solitary wave is investigated. The pert graphical view of the results has been presented for illustration. It is observed that increase in the relativistic streaming factor causes the soliton amplitude to thrive and its width shrinks. The soliton amplitude and width decline as the ion to electron temperature ratio is increased. The increase in positron concentration results in reduction of soliton amplitude. The soliton amplitude enhances as the electron to positron temperature ratio is increased. Our results may have relevance in the understanding of astrophysical plasmas.

On the linear and nonlinear characteristics of electrostatic solitary waves propagating in magnetized electron–positron–ion plasmas

Both linear and nonlinear propagation of electrostatic solitary waves (ESWs) in magnetized electron–positron–ion (e-p-i) plasmas are analyzed. The electrons and positrons are assumed to be dynamic, whereas positively charged ions are considered stationary. Using the reductive perturbation method, a Zakharov–Kuznetsov (ZK) equation is derived and exact soliton solutions are presented. It is found that both compressive and rarefactive ESWs can propagate. The conditions of transitions from compressive to rarefactive ESWs are specified. The nature of these electrostatic solitary waves structures which depends on the magnetic field, the obliqueness, the ion-to-electron number density ratio, and the positron-to-electron temperature ratio, are discussed.

Arbitrary amplitude solitary waves in plasmas with dust grains of opposite polarity and non-thermal ions

AbstractThe existence of large amplitude solitary waves in a plasma comprised of a cold negative dust fluid, adiabatic positive dust fluid, Boltzmann electrons and non-thermal ions is theoretically investigated. Different regions in parameter space that correspond to different values of the ratio of the charge-to-mass ratios of the positive and negative dust grains have been identified where either negative or positive potential solitary wave structures occur and a region where coexistence of negative and positive potential solitary waves is supported.

Nonlinear wave motion and complexity

Contemporary complexity science deals with problems which involve many variables interacting with each other in such a way that a new quality appears. An important cornestone of complex systems is nonlinearity. In this paper nonlinear wave motion in microstructured solids is analysed from the viewpoint of complexity. The basic models are derived by using the concept of internal variables which are related to dissipation inequality. The scale dependence results in wave hierarchies where dispersive effects are important. In such nonlinear models solitary wave structures may emerge – a typical sign of a new quality characteristic of complexity. In addition, examples from biophysics are presented, which demonstrate clearly the similarity to the ideas of complexity shown for waves in solids.

Electrostatic solitary ion waves in dense electron-positron-ion magnetoplasma

The nonlinear coupled ion-acoustic and ion-cyclotron waves propagating obliquely to the external magnetic field in dense collisionless electron-positron-ion magnetoplasma are investigated using Sagdeev potential method. A semiclassical approach is used. Electrons and positrons are treated as degenerate Fermi gases described by Thomas–Fermi density distribution and ions behave as classical gas. It is found that the presence of degenerate positrons in a dense Thomas–Fermi plasma significantly modifies the structure of solitary waves by restricting the electrostatic potential to a certain maximum value which depends upon the concentration of positrons in the system. It is also noted that only subsonic humplike solitary waves can exist and for a given angle of propagation, the presence of degenerate positrons diminishes the amplitude as well as width of the solitary wave.

Alternative ion-acoustic solitary waves in magnetized low beta plasma consisting of warm adiabatic ions, nonthermal electrons, and electrons having a vortexlike distribution

The solitary wave structures of the ion-acoustic waves propagating obliquely to an external uniform magnetic field have been considered in a low beta plasma consisting of warm adiabatic ions, nonthermal electrons, due to Cairns et al. [Geophys. Res. Lett. 22, 2709 (1995)], which generates the fast energetic electrons and electrons having a vortexlike distribution, due to Schamel [Plasma Phys. 13, 491 (1971); 14, 905 (1972)], taking care of both free and trapped electrons, immersed in a uniform static magnetic field. The nonlinear dynamics of ion-acoustic waves in such a plasma is shown to be governed by Schamel’s modified Korteweg–de Vries–Zakharov–Kuznetsov equation. When the coefficient of the nonlinear term of this equation vanishes, the vortexlike velocity distribution function of electrons simply becomes the isothermal velocity distribution function of electrons and the nonlinear behavior of the same ion-acoustic wave is described by a Korteweg–de Vries–Zakharov–Kuznetsov (KdV-ZK) equation. A combined Schamel’s modified Korteweg–de Vries–Zakharov–Kuznetsov (S-KdV-ZK) equation is shown to describe the nonlinear behavior of ion-acoustic wave when the vortexlike velocity distribution function of electrons approaches the isothermal velocity distribution function of electrons, i.e., when the contribution of trapped electrons tends to zero. This combined S-KdV-ZK equation admits an alternative solitary wave solution having profile different from sech4 or sech2. The condition for the existence of this alternative solitary wave solution has been obtained. It is found that this alternative solitary wave solution approaches the solitary wave solution (sech2-profile) of the KdV-ZK equation when the contribution of trapped electrons tends to zero.

Objective Reduction Solutions to Higher-Order Boussinesq System in (2+1)-Dimensions

With the help of an objective reduction approach (ORA), abundant exact solutions of (2+1)-dimensional higher-order Boussinesq system (including some hyperboloid function solutions, trigonometric function solutions, and a rational function solution) are obtained. It is shown that some novel soliton structures, like single linearity soliton structure, breath soliton structure, single linearity y-periodic solitary wave structure, libration dromion structure, and kink-like multisoliton structure with actual physical meaning exist in the (2+1)-dimensional higher-order Boussinesq system.

The novel solitary wave structures and interactions in the (2 + 1)-dimensional Kortweg-de Vries system

Using symbolic and algebra computation, the extended tanh-function method (ETM) based on mapping method is further extended. The new variable separation solutions of the (2 + 1)-dimensional Korteweg-de Vries (KdV) system are derived. From the periodic wave solution and by selecting appropriate functions, the evolutional behaviors of dromions and compactons on the background of Jacobian elliptic wave and their interaction behaviors are investigated.

Higher order solutions to ion-acoustic solitons in a weakly relativistic two-fluid plasma

The nonlinear wave structure of small amplitude ion-acoustic solitary waves (IASs) is investigated in a two-fluid plasma consisting of weakly relativistic streaming ions and electrons. Using the reductive perturbation theory, the basic set of governing equations is reduced to the Korteweg–de Vries (KdV) equation for the lowest order perturbation. This analysis is further extended using the renormalization technique for the inclusion of higher order nonlinear and dispersive effects for better accuracy. The effect of higher order correction and various parameters on the soliton characteristics is investigated and also discussed.