Solitary Wave Structures Research Articles

Structure and evolution of magnetohydrodynamic solitary waves with Hall and finite Larmor radius effects.

Nonlinear and low-frequency solitary waves are investigated in the framework of the one-dimensional Hall-magnetohydrodynamic model with finite Larmor effects and two different closure models for the pressures. For a double adiabatic pressure model, the organization of these localized structures in terms of the propagation angle with respect to the ambient magnetic field θ and the propagation velocity C is discussed. There are three types of regions in the θ-C plane that correspond to domains where either solitary waves cannot exist, are organized in branches, or have a continuous spectrum. A numerical method valid for the two latter cases, which rigorously proves the existence of the waves, is presented and used to locate many waves, including bright and dark structures. Some of them belong to parametric domains where solitary waves were not found in previous works. The stability of the structures has been investigated by performing a linear analysis of the background plasma state and by means of numerical simulations. They show that the cores of some waves can be robust, but, for the parameters considered in the analysis, the tails are unstable. The substitution of the double adiabatic model by evolution equations for the plasma pressures appears to suppress the instability in some cases and to allow the propagation of the solitary waves during long times.

Nonlinear dust magnetosonic waves in collisional plasma

The excitations and damping of nonlinear dust magnetosonic waves in dissipative plasma are investigated. The dynamics of negatively charged dust particles is considered. The dissipation is taken due to dust neutral collisions. The ions and electrons are inertialess on dust dynamic scale. The temperature of ions and electrons is also taken into account. The linear dispersion charteristics of dust magnetosonic waves are discussed for different values of plasma parameters. For this purpose we have derived Damped Korteweg de Vries (DKdV) equation by applying the reductive perturbation method. For weak dissipation the analytical solution of DKdV is presented. For the numerical solution, we apply a two-level finite difference scheme with the help of the Runge-Kutta method. The effects of variations of different plasma parameters on the damping of nonlinear dust magnetosonic solitary wave structures are discussed.

Damped electrostatic ion acoustic solitary wave structures in quantum plasmas with Bohm potential and spin effects

Nonlinear properties of ion acoustic solitary waves are studied in the case of dense magnetized plasmas. The degenerate electrons with relative density effects from their spin states in the same direction and from equally probable up and down spinning states are taken up separately. Quantum statistical as well as quantum tunneling effects for both types of electrons are taken. The ions have large inertia and are considered classically, whereas the electrons are degenerate. The collisions of ions and electrons with neutral atoms are considered. We derive the deformed Korteweg de–Vries (DKdV) equation for small amplitude electrostatic potential disturbances by employing the reductive perturbation technique. The Runge–Kutta method is applied to solve numerically the DKdV equation. The analytical solution of DKdV is also presented with time dependence. We discuss the profiles for velocity, amplitude, and time variations in solitons for the cases when all the electrons are spinning in the same direction and for the case when there is equal probability of electrons having spin up and spin down. We have found that the wave is unstable because of the collisions between neutral gas molecules and the charged plasmas particles in the presence of degenerate electrons.

An elog-KdVB dynamics in non-thermal solar plasmas

This paper deals with a continued study on the basis of the gravito-electrostatic sheath (GES) model to explore the excitation of solitary and shock-like wave structures evolving in the non-thermal solar plasmas. The method applied here is based on a nonlinear local perturbation analysis over the GES structure equations designed in a thermostatistically modified form to arrive at an extended logatropic Korteweg-de Vries-Burgers (elog-KdVB) equation with a unique linear derivative source, which has in principle, a special set of multiparametric coefficients dependent on the diversified solar plasma parameters. A constructive numerical integration of the elog-KdVB equation yields the excitation of rarefactive shock-like wave patterns supported in the solar plasmas. Their noticeable unique characteristic feature is the naturalistic existence of distorted non-uniform tails. The shock-wave amplitude increases with the increase in the thermostatistical power (κ), and vice versa. In contrast, the shock-tail width decreases with the increase in the thermostatistical distribution power (κ), and vice versa. It implicates that the shock-tail width vanishes in the Boltzmann thermostatistical limit (). The corresponding gradients, phase portraits, and curvature dynamics associated with the fluctuations are illustratively depicted. The microphysical details behind the dynamics are analyzed. The elog-KdVB dynamical results explored are bolstered with the reinforcement of the earlier multispace satellitic observations and original probe measurements reported elsewhere. The non-trivial implications and applications are summarily highlighted in the real helioseismic contextual linkage.

Solutions of nonplanar KP-equations for dusty plasma system with GE-method

The propagation of three-dimensional nonlinear dust acoustic waves in a dusty plasma consisting of positive and negative dust grains as well as Boltzmann distributed electrons and ions is investigated. Using a reductive perturbation method, Cylindrical Kadomtsev-Petviashvili and Spherical Kadomtsev-Petviashvili equations, appropriate for describing the evolution of the system, are derived. The Generalized Expansion method is used to find the various solutions of the obtained nonlinear Kadomtsev-Petviashvili equations. New classes of triangular, hyperbolic solitary, rational, and Jacobi elliptical type solutions are obtained and graphically presented. It is found that the proposed dusty plasma model can support solitary waves with compressive and rarefactive potential pulses. Moreover, the effects of plasma parameters on this solitary wave structure are investigated. The current findings are applied to a cosmic-type plasma in different regions of space, viz. cometary tails, mesosphere, and Jupiter's magnetosphere as well as laboratory-type plasma such as low temperature experiments, where a dusty plasma with opposite polarity is dominant.

Dust‐ion‐acoustic solitary waves in a magnetized dusty pair‐ion plasma with Cairns‐Gurevich electrons and opposite polarity dust particles

The nonlinear dust‐ion‐acoustic (DIA) solitary structures have been studied in a dusty plasma, including the Cairns‐Gurevich distribution for electrons, both negative and positive ions, and immobile opposite polarity dust grains. The external magnetic field directed along the z‐axis is considered. By using the standard reductive perturbation technique and the hydrodynamics model for the ion fluid, the modified Zakharov–Kuznetsov equation was derived for small but finite amplitude waves and was provided the solitary wave solution for the parameters relevant. Using the appropriate independent variable, we could find the modified Korteweg–de Vries equation. By plotting some figures, we have discussed and emphasized how the different plasma values, such as the trapping parameter, the positive (or negative) dust number density, the non‐thermal electron parameter, and the ion cyclotron frequency, can influence the solitary wave structures. In addition, using the bifurcation theory of planar dynamical systems, we have extracted the centre and saddle points and illustrated the phase portrait of such a system for some particular plasma parameters. Finally, we have graphically investigated the behaviour of the solitary energy wave by changing the plasma values as well as by calculating the instability criterion; we have also discussed the growth rate of the solitary waves. The results could be useful for studying the physical mechanism of nonlinear propagation of DIA solitary waves in laboratory and space plasmas where non‐thermal electrons, pair‐ions, and dust particles can exist.

Breathers and the Dynamics of Solutions in KdV Type Equations

In this paper our first aim is to identify a large class of non-linear functions $\,f(\cdot)\,$ for which the IVP for the generalized Korteweg-de Vries equation does not have breathers or "small" breathers solutions. Also we prove that all small, uniformly in time $L^1\cap H^1$ bounded solutions to KdV and related perturbations must converge to zero, as time goes to infinity, locally in an increasing-in-time region of space of order $t^{1/2}$ around any compact set in space. This set is included in the linearly dominated dispersive region $x\ll t$. Moreover, we prove this result independently of the well-known supercritical character of KdV scattering. In particular, no standing breather-like nor solitary wave structures exists in this particular regime.

Collisional effects in negative ion plasmas in the presence of degenerate electrons

Ion acoustic solitary wave structures in negative ion plasmas in the presence of degenerate electrons are investigated. The collisions of positive ions, negative ions, and electrons with neutrals are considered. The Damped Korteweg-de Vries (DKdV) equation is derived by using reductive perturbation method. The time dependent solution of DKdV is presented. Different combinations of the negative ion plasmas in the presence of degenerate electrons are considered for numerical analyses. The effects of variations of different plasmas parameters on the propagation characteristics of the damped solitary wave structure are discussed.

Modeling of emerged semi-circular breakwater performance against solitary waves using SPH method

The semicircular breakwater (SBW) is a composite breakwater consisting of a hollow empty reinforced concrete caisson seated on the rubble mound breakwater. In this research, smoothed particle hydrodynamics (SPH) method was used to examine the run-up and overtopping of solitary waves on SBW. At first the SPH model was validated for regular wave–SBW interaction against experimental results. Comparisons showed that the present modified numerical model has a good agreement with experimental data. Parametric study was then performed on the effect of water depth and wave height of the single solitary waves and height of the rubble mound on wave run-up. Furthermore, double solitary waves were generated to study their interaction with SBW by the model. Run-up and reflection coefficient for double solitary wave–structure interaction was then investigated. The results show that in sum run-up in double solitary wave mode is smaller than that of single solitary wave. Moreover, the second solitary wave run-up is smaller than that of the first solitary wave in double solitary wave train. Overtopping discharge of double solitary wave is nearly constant for τ/T greater than 1.3, where τ/T is the ratio of time distance between wave crests of double wave to effective period of single solitary wave. Also overtopping discharge decreases with increasing in τ/T for its value smaller than 1.3. The results show that this model is a useful tool for simulating the interaction of solitary waves–structures with complicated geometry.

Structure of equatorial envelope Rossby solitary waves with complete Coriolis force and the external source

In this article, the behavior of the equatorial envelope Rossby solitary waves with complete Coriolis force and the external source are investigated analytically. By the asymptotic method of multiple scales and perturbation expansions, a new cubic nonlinear Schrödinger equation with complete Coriolis force and the external source is derived to describe the evolution of equatorial envelope Rossby solitary waves. The equation is different from the common Schrödinger equation, it is more suitable for describing envelope Rossby solitary waves when the horizontal component Coriolis force is stronger near the equator. Using the equation, the features of generalized beta, the horizontal component of Coriolis force and the external source are presented. And then various periodic structures for equatorial envelope Rossby solitary waves are obtained with the help of Jacobi elliptic functions and elliptic equation. Particularly, the solution of envelope Rossby solitary waves is obtained and graphical presentations are shown for Rossby solitary waves amplitude with the different Coriolis parameters. It is pointed out that with decreasing of Coriolis parameter λ, the amplitude of Rossby solitary waves decreases, whereas the propagating frequency is unchanged. And we find that the periodic solution of the nonlinear Schrödinger equation have different structures with a phase-locked diabatic heating source and without a source.

Effect of electron temperature on small-amplitude electron acoustic solitary waves in non-planar geometry

Effects of electron temperature on the propagation of electron acoustic solitary waves in plasma with stationary ions, cold and superthermal hot electrons is investigated in non-planar geometry employing reductive perturbation method. Modified Korteweg–de Vries equation is derived in the small amplitude approximation limit. The analytical and numerical calculations of the KdV equation reveal that the phase velocity of the electron acoustic waves increases as one goes from planar to non planar geometry. It is shown that the electron temperature ratio changes the width and amplitude of the solitary waves and when electron temperature is not taken into account,our results completely agree with the results of Javidan & Pakzad (2012). It is found that at small values of \(\tau \), solitary wave structures behave differently in cylindrical (\(\text {m} = 1\)), spherical (\(\text {m} = 2\)) and planar geometry (\(\text {m} = 0\)) but looks similar at large values of \(\tau \). These results may be useful to understand the solitary wave characteristics in laboratory and space environments where the plasma have multiple temperature electrons.

Study of small amplitude ion-acoustic solitary wave structures and amplitude modulation in e–p–i plasma with streaming ions

AbstractBy using reductive perturbation technique we have studied the linear and non-linear properties of ion-acoustic solitary structures in a three-component plasma containing non-thermal electrons and Boltzmann positrons and a comparatively cold ion which has got a streaming motion. The Korteweg–de Vries equation has been obtained and the dependence of small amplitude solitary structures on various plasma parameters such as streaming velocity (v0), non-thermal parameter (β), reciprocal of electron temperature (χ), positron density (p), Mach number (M), and ion density (δ) have been studied. The possibility of formation of enveloping soliton and its characteristic features are further investigated by deriving the non-linear Schrödinger equation.

Cylindrical fast magnetosonic solitary waves in quantum degenerate electron-positron-ion plasma

The nonlinear properties of fast magnetosonic solitary waves in a quantum degenerate electron-positron (e-p) plasma in the presence of stationary ions for neutralizing the plasma background of bounded cylindrical geometry were studied. By employing the standard reductive perturbation technique and the quantum hydrodynamic model for the e-p fluid, the cylindrical Kadomtsev-Petviashvili (CKP) equation was derived for small, but finite, amplitude waves and was given the solitary wave solution for the parameters relevant to dense astrophysical objects such as white dwarf stars. By a suitable coordinate transformation, the CKP equation can be solved analytically. An analytical solution for magnetosonic solitons and periodic waves is presented. The numerical results reveal that the Bohm potential has a main effect on the periodic and solitary wave structures. By increasing the values of the plasma parameters, the amplitude of the solitary wave will be increased. The present study may be helpful in the understanding of nonlinear electromagnetic soliton waves propagating in both laboratory and astrophysical plasmas, and can help in providing good agreement between theoretical results and laboratory plasma experiments.

Analytical Solitary Wave Solution of the Dust Ion Acoustic Waves for the Damped Forced Korteweg–de Vries Equation in Superthermal Plasmas

Abstract Analytical solitary wave solution of the dust ion acoustic (DIA) waves was studied in the framework of the damped forced Korteweg–de Vries (DFKdV) equation in superthermal collisional dusty plasmas. The reductive perturbation technique was applied to derive the DKdV equation. It is observed that both the rarefactive and compressive solitary wave solutions are possible for this plasma model. The effects of κ and the strength (f 0) and frequency (ω) of the external periodic force were studied on the analytical solitary wave solution of the DIA waves. It is observed that the parameters κ, f 0 and ω have significant effects on the structure of the damped forced DIA solitary waves. The results of this study may have relevance in laboratory plasmas as well as in space plasmas.

Dust ion acoustic waves in four component magnetized dusty plasma with effect of slow rotation and superthermal electrons

Dust ion acoustic waves are investigated in four component magneto-rotating dusty plasma comprising opposite polarity dust grains, ions, and nonthermal electrons using the concept of one fluid and two fluid models. The Zakharov-Kuznetsov equation is derived using the reductive perturbation technique to study the nonlinear solitary wave structures. The numerical results show that the superthermality of electrons affects both amplitude and width of the solitary waves while the rotational frequency has a small impression on the width. It is shown that the solitary wave changes its potential from positive to negative at a critical value of the superthermal parameter. It is also observed that the inertial role of dust grains flourishes the effect of rotational frequency and also changes the critical value of the superthermal parameter where the positive/negative potential solitary waves exist.

Solitary waves in a homogeneous plasma

Conditions of the electron soliton existence are determined on the base of a simple model related to inhomogeneous nonlinear azimuthally symmetric wave processes in uniform plasmas. Connections between initial–boundary values and nonlinear wave parameters established define the magnitudes of all necessary characteristics for the case when the original equations have the solution of the solitary wave structure.

Generation of ion acoustic solitary waves through wave breaking in superthermal plasmas

Space plasmas provide abundant evidence of a highly energetic particle population that results in a long-tailed non-Maxwellian distribution. Such plasmas can be effectively modeled with kappa distribution. The superthermal population in the tail of kappa distribution can have significant effects on the wave dynamical processes. We perform the fluid simulations to examine the effects of superthermal populations on the breaking of the electrostatic ion-acoustic (IA) wave, which is the most fundamental mode, existing in the unmagnetized plasmas. We construct a fluid model for exciting IA waves by employing a kappa distribution function for the superthermal population of electrons along with inertial cold ions (protons). We focused on the nonlinear excitations; in the form of ion acoustic solitary wave (IASW) structures formed through the process of wave breaking, and investigated the role of superthermal electron population in the initiation of the steepening, wave breaking, and propagation characteristics of the IASWs in plasma. From the output of the simulation, we established the criteria for the steepening time based on the variations in the phase velocity of the IASWs. Furthermore, we examined the maximum ponderomotive potential and ponderomotive frequency during the wave breaking process. We found that the time corresponding to the peak in the maximum ponderomotive potential is the time of the initialization of the wave breaking process. We present a detailed investigation of the role of the ponderomotive forces acting on the plasma at each time step, which explains the physics of the wave breaking in nonthermal plasmas.

Electrostatic solitary waves in an electron-positron pair plasma with suprathermal electrons

The nonlinear propagation of electrostatic solitary waves is studied in a collisionless electron-positron pair plasma consisting of adiabatic cool electrons, mobile cool positrons (or electron holes), hot suprathermal electrons described by a κ distribution, and stationary ions. The linear dispersion relation derived for electrostatic waves demonstrates a weak dependence of the phase speed on physical conditions of positrons in appropriate ranges of parameters. The Sagdeev's pseudopotential approach is used to obtain the existence of electrostatic solitary wave structures, focusing on how their characteristics depend on the physical conditions of positrons and suprathermal electrons. Both negative and positive polarity electrostatic solitary waves are found to exist in different ranges of Mach numbers. As the positrons constitute a small fraction of the total number density, they slightly affect the existence domains. However, the positrons can significantly change the wave potential at a fixed soliton speed. The results indicate that the positive potential can largely be grown by increasing the electron suprathermality (lower κ) at a fixed true Mach number. It is found that a fraction of positrons maintain the generation of positive polarity electrostatic solitary waves in the presence of suprathermal electrons in pair plasmas.

Study of ion-acoustic solitary wave structures in multi-component plasma containing positive and negative ions and q-exponential distributed electron beam

AbstractUsing reductive perturbation technique, small-amplitude ion-acoustic solitary wave has been investigated in multi-component dense plasma, in which an electron beam propagates along the general streaming motion. The electrons in plasma have the q-exponential distribution. The positive and negative ions follow a regular Maxwellian distribution. It has been found that the positive and negative ion densities as well as the beam concentration have significant effect on the formation and properties of solitary structures. The streaming velocities of corresponding particles also have pronounced effect on the features of the solitons.

Arbitrary amplitude ion-acoustic solitary waves in a two-temperature nonextensive electron plasma

Effects of presence of ions on the existence and structure of arbitrary amplitude ion-acoustic solitary waves in a plasma consisting of thermal ions and two-temperature nonextensive electrons are investigated. It is shown that solitons of both polarity (compressive and rarefactive) can exist in such a plasma, depending on the range of the plasma parameters. Also, it is seen that the maximum amplitude and the width of both soliton types depend sensitively on the temperature and concentration of ions. To better understand the role of positive ions, the presented model is reduced to a Maxwellian plasma and the results are compared to their Maxwellian counterparts.