Soliton Width Research Articles

Weakly Nonlinear Dust-Ion-Acoustic Solitons in an Electronegative Collisionless Dusty Plasma With Cairns–Gurevich Distributed Electrons

The problem of dust-ion-acoustic (DIA) solitons is addressed in an electronegative collisionless dusty plasma with the presence of trapped-nonthermal electrons. To do this, we revisited the Cairns–Gurevich distribution that describes, concurrently, the evolution of the energetic electrons and those trapped in the plasma potential and analytically expressed its corresponding density. The modifications, due to the presence of this trapped nonthermal density, arising in small-amplitude DIA solitons propagation associated with both space and experimental plasmas are analyzed. In particular, we have found that, in both cases, a proportion of trapped nonthermal electrons relatively significant makes the solitary structure less spiky. Besides, we have shown that the amplitude and width of the experimental plasma soliton seem more affected due to the low ionic mass ratio.

Solitons propagation dynamics in a saturable PT-symmetric fractional medium

In the current research, the propagation of solitons in a saturable PT-symmetric fractional system is studied by solving nonlinear fractional Schrödinger equation. Three numerical methods are employed for this purpose, namely Monte Carlo based Euler–Lagrange variational schema, split-step method, and extrapolation approach. The results show good agreement and accuracy. The effect of different parameters such as potential depth, Levy indices, and saturation parameter, on the physical properties of the systems such as maximum intensity and soliton width oscillations are considered.

Interaction of Airy beams modeled by the fractional nonlinear cubic-quintic Schrödinger equation

We investigate theoretically and numerically the interaction of Airy beams modeled by fractional nonlinear cubic-quintic Schrödinger equation. By considering fractional diffraction effect, when the initial beam interval between the two Airy beams is large enough, it is found that two in-phase Airy beams attract and repel each other, and two out-of-phase beams repel each other. This is different from the interaction of two Airy beams with large interval in standard nonlinear Schrödinger equation, where the two beams display a weak interaction. For smaller interval, single breathing soliton and symmetric breathing soliton pairs are formed in the in-phase and out-of-phase cases, respectively. As the Lévy index decreases, for the single breathing soliton, the oscillation becomes stronger, the mean peak intensity increases, and the soliton width decreases, for the symmetric breathing soliton pair, the width becomes narrower, and the repulsion between the two Airy components becomes stronger. Besides, the quintic defocusing strength will modulate the interaction of Airy beams. When the strength coefficient increases, the width of the breathing soliton formed in the in-phase case becomes wider, the repulsion between the two beams in the out-of-phase case increases, as well as the width of the soliton pair becomes wider. The work may provide new control methods on the interaction of Airy beams.

Obliquely overtaking collisions of electrostatic N-soliton in the Thomas-Fermi dense magnetoplasma

Overtaking collision of unidirectional dust acoustic waves in the Thomas-Fermi dense magnetoplasma has been investigated. The system consists of classical negatively charged dust particles with degenerate electrons and ions. Nonlinear Korteweg-de Vries (KdV) equation that characterizing the dust acoustic solitons in such a plasma model is derived. The system admits only rarefactive solitary waves. Hirota's bilinear method is used to investigate the overtaking collision of two and three-soliton solutions. The exchange of energies due to the overtaking collisions is affected by physical parameters such as the electron equilibrium density, the dust temperature, and the obliquity angle. This causes the solitons behavior to be alternated. The amplitude, and width increase as the dust temperature and electron density decrease or when the dust density increases. The magnetic field affects only the soliton's width. The phase shifts are also affected by the system parameters. The current study is an attempt to illuminate the properties of N-soliton in Thomas-Fermi dense magnetoplasma that are applicable in compact astrophysical objects such as white dwarfs and high-intensity laser-solid matter interaction experiments.

Quantum Electron Acoustic Solitons and Double Layers with κ-deformed Kaniadakis Distributed Electrons

The present investigation is dedicated to the study of propagation characteristics of electron acoustic (EA) waves and double layers in the quantum plasma system containing inertialess hot electrons and inertial cold electrons with stationary ions forming the charge neutralizing background. It is assumed that hot electrons follow κ-deformed Kaniadakis distribution as governed by the parameter κ. Using the appropriate stretched coordinates and reductive perturbation method (RPM) the Korteweg-de Vries (KdV) and modified KdV (mKdV) equations have been derived. For the sake of analysis, a limit of range of deformation parameter (κ) has been set as -0.4≤κ≤0.4. For the defined range, it has been observed that plasma system supports rarefactive solitary structures. The amplitude and width of KdV soliton have been significantly affected by the quantum effects and remains unaffected by the deformation parameter (κ). The analysis was further extended to the derivation of mKdV equation to investigate the existence of small amplitude double layers (DLs). Only negative potential DLs are found to exist whose dynamics significantly depends on deformation parameter (κ), quantum effects (H) and hot to cold electron density ratio (α). The outcome of the present discourse may be helpful to understand the use of generalized entropies in the environment of plasma physics.

Novel optical solitons to the perturbed Gerdjikov–Ivanov equation via collective variables

The objective of this manuscript is to study the collective variable (CV) technique to explore an important form of Schrödinger equation known as the Gerdjikov–Ivanov (GI) equation which expresses the dynamics of solitons for optical fibers in terms of pulse parameters. These parameters are temporal position, amplitude, width, chirp, phase, and frequency known as CVs. This is an effective and dynamic mathematical gadget to obtain soliton solutions of non-dimensional as well as perturbed GI equations. Moreover, an established numerical scheme that is the fourth-order Runge–Kutta method is exerted for the numerical simulation of the revealing coupled system of six ordinary differential equations which represent all the CVs included in the pulse ansatz. The CV approach is used to determine the evolution of pulse parameters with the propagation distance and illustrated them graphically. Furthermore, figures show the compelling periodic oscillations of pulse chirp, width, frequency and amplitude of soliton. For various values of super-Gaussian pulse parameters, the numerical behavior of solitons to illustrate variations in CVs is provided. Other significant aspects with regards to the current investigation are also inferred.

The characteristics of daughter waves emerging from colliding solitary waves in astrophysical plasma media

ABSTRACT The aim is to state the properties of ion acoustic solitary waves in course of collision and extract characteristics of the daughter wave in a magnetized electron–ion plasma. The magnetized plasma medium that is a constituent of white dwarfs and astrophysical plasmas that possesses relativistically degenerate electrons and thermal ions in the presence of a constant background magnetic field. The model is based on the extended Poincaré–Lighthill–Kuo (ePLK) method where a set of Korteweg–de Vries equations is obtained to show the phase shifts of colliding waves together with the amplitude and width of the born daughter solitary waves. The numerical results and presented figures regarding the amplitude and width of solitons provide a description of the influence of plasma parameters on soliton interactions, namely ion to electron temperature ratio (σi), ion cyclotron frequency (ωci), and angle between magnetic field and collision line (θ) together with their interplay in shaping the character of solitary waves. It is concluded that only rarefactive electrostatic non-linear waves are able to propagate in such plasma media. The daughter wave amplitude possesses a scaling behaviour regarding the impact angle. Interplay of the parameters on the phase shifts is presented. Ratio of amplitude and width of the daughter wave is directly proportional to the background field, the impact angle controls its maximum. It is observed that the magnetic field elevates ratio of the solitary wave amplitude to width leading it to a shorter life and hence interaction range with neighbouring sites.

Dust–Acoustic Envelope Solitons in an Electron-Depleted Plasma

A theoretical investigation of the modulational instability (MI) of dust–acoustic waves (DAWs) by deriving a nonlinear Schrodinger equation in an electron-depleted opposite polarity dusty plasma system containing non-extensive positive ions is presented. The conditions for MI of DAWs and formation of envelope solitons are investigated. The sub-extensivity and super-extensivity of positive ions are seen to change the stable and unstable parametric regimes of DAWs. The addition of dust grains causes changes the width of both bright and dark envelope solitons. The findings of this study can help understanding the nonlinear features of DAWs in Martian atmosphere, cometary tails, solar system, laboratory experiments, etc.

Interactions of Soliton in Weakly Nonlocal Nonlinear Media

Solitary waves or solitons is a nonlinear phenomenon which has been studied intensively due to its application in solid-state matter such as Bose-Einstein condensates state, plasma physics, optical fibers and nematic liquid crystal. In particular, the study of nonlinear phenomena occurs in the structure of waves gained interest of scholars since their discovery by John Russell in 1844. The Nonlinear Schrödinger Equation (NLSE) is the theoretical framework for the investigation of nonlinear pulse propagation in optical fibers. Nonlocality can be found in an underlying transport mechanisms or long-range forces like electrostatic interactions in liquid crystals and many-body interactions with matter waves in Bose-Einstein condensate or plasma waves. The length of optical beam width and length of response function are used to classify nonlocality in optical materials. The nonlocality can be categorized as weak nonlocal if the width of the optical beam broader than the length of response function and if the width of the optical beam is narrower than the length of response function, it is considered as highly nonlocal. This work investigates the interactions of solitons in a weakly nonlocal Cubic NLSE with Gaussian external potential. The variational approximation (VA) method was employed to solve non integrable NLSE to ordinary differential equation (ODE). The soliton parameters and the computational program are used to simulate the propagation of the soliton width and its center-of-mass position. In the presence of Gaussian external potential, the soliton may be transmitted, reflected or trapped based on the critical velocity and potential strength. Direct numerical simulation of Cubic NLSE is programmed to verify the results of approximation method. Good agreement is achieved between the direct numerical solution and VA method results.

Ion-acoustic solitons in negative ion plasma with relativistic degenerate electrons and positrons

In this paper, the oblique propagation of the ion-acoustic quantum soliton in polarized quantum plasma including relativistic degenerate electrons and positrons is studied. By using the reductive perturbation method, we derived the ZK equation for this model. This equation shows that in presence of the negative ion there are two slow and fast ion-acoustic modes. Our numerical results indicate that there are only compressive and refractive solitons for fast and slow modes, respectively. The effect of the negative ion parameters on the amplitude and width of the ion-acoustic quantum soliton are studied, as well.

A mechanism for electrostatic solitary waves observed in the reconnection jet region of the Earth’s magnetotail

• An ion-acoustic soliton model for the ESWs in the reconnection jet region. • Observed plasma parameters used as input for the model, there is no free parameter. • Slow and fast ion-acoustic solitons can exist in the reconenction jet plasma. • Good agreement between theoretical predictions and observed properties of ESWs. Electrostatic solitary waves (ESWs) have been observed in the reconnection jet region in the Earth’s magnetotail by the Magnetospheric Multiscale spacecraft (MMS). A mechanism for the reconnection jet ESWs is proposed in terms of slow and fast ion-acoustic solitons. At the time of occurrence of ESWs, no hot plasmasheet ions were observed. Based on the observations, the reconnection jet plasma is modeled by a three-component magnetized plasma consisting of hot electrons and two cold ion beams streaming parallel and anti-parallel to the magnetic field, B respectively. The model is based on the Sagdeev pseudopotential technique, and it predicts four types of ion-acoustic solitons, namely, two fast and two slow ion-acoustic solitons, where one of each type propagates parallel and another anti-parallel to the ambient magnetic field, respectively. The theoretical model predicts bipolar electric fields with amplitudes in the range of ≈ (3–69) mV m −1 , positive potentials with amplitudes of ≈ (51–539) V, and the soliton widths of ≈ (4.5–10.3) Debye lengths. These predictions are in good agreement with the observed characteristics of ESWs in the reconnection jet region.

Dispersion and phase managed optical soliton solutions of a nonautonomous (3+1)-dimensional coupled nonlinear Schrödinger equation

The complex amplitude ansatz method and He's semi-inverse method have been used to investigate the optical soliton solutions of a nonautonomous (3+1)-dimensional coupled non-linear Schrödinger (NLS) equation. The effect of the time-dependent dispersion (TD) and the phase modulation (PM) coefficients in the equation has been analyzed. The intensity profiles of the soliton solutions have been obtained by assigning different test functions to the coefficients and distinct values to the parameters, which help to understand the physical characteristics of the solutions. The intensities of two circularly polarized waves have bright, dark, parabolic, dark-bright, parabolic-bright, bright-singular, homoclinic and breather solitons that depend significantly on the dispersion and phase modulation. Some of the obtained soliton solutions are novel and did not exist in the earlier studies. It is found that the optical soliton velocity and frequency are dependent on wave numbers and dispersion of the medium but are free from the phase modulation. Moreover, the amplitude of the solitons are managed by dispersion and phase modulation both but the soliton width remains constant. The results in this study may be used for experimental investigation of transmission of dispersion and phase managed optical soliton in non-linear optical fiber.

Effect of non-thermal electrons on ion-acoustic dressed solitons in unmagnetised plasmas

Nonlinear propagation of an ion-acoustic dressed soliton is studied in unmagnetised plasma consisting of ion, positron and non-thermal electron. The exact soliton solution is derived using the reductive perturbation method (RPM) with the help of renormalisation procedure. This exact solution reduces to the dressed soliton solution when Mach number is expanded in terms of soliton velocity. The effects of non-thermal electrons, soliton velocity and Mach number on the characteristics (amplitude, width and product of amplitude and square of width) of the KdV soliton, core structure, dressed soliton and exact soliton are discussed in detail.

Nonlinear dust acoustic waves in an inhomogeneous magnetized quantum dusty plasma

Propagations of nonlinear quantum dust acoustic waves (QDAWs) in an inhomogeneous magnetized dusty plasma model which is three-dimensional collisionless, and having number density gradients of its components along x-direction is investigated. This model consisting of ions, electrons and charged dust particles in the presence of an external static magnetic field. The reductive perturbation method was adopted to derive the modified Zakhavov Kusnetsov equation (MZK) whose coefficients are space dependent. The incorporation of inhomogeneity caused by nonuniform equilibrium values of particle density leads to a significant modification to the nature of nonlinear QDAWs. Solutions for the MZK equation are obtained by using a generalized expansion method. The solutions have two parts; amplitude factor and the superposition of bell-shaped solitary wave. The soliton amplitude, width, and velocity depends on the plasma inhomogeneities. Findings in these numerical investigations should be useful in understanding the astrophysical plasmas and ultra small micro- and nano-electronic devices.

Dust-acoustic envelope solitons and rogue waves in an electron depleted plasma

A theoretical investigation of the modulational instability (MI) of dust-acoustic waves (DAWs) by deriving a nonlinear Schr\"{o}dinger equation in an electron depleted opposite polarity dusty plasma system containing non-extensive positive ions has been presented. The conditions for MI of DAWs and formation of envelope solitons have been investigated. The sub-extensivity and super-extensivity of positive ions are seen to change the stable and unstable parametric regimes of DAWs. The addition of dust grains causes to change the width of both bright and dark envelope solitons. The findings of this study may be helpful to understand the nonlinear features of DAWs in Martian atmosphere, cometary tail, solar system, and in laboratory experiments, etc.

The role of constant vorticity on weakly nonlinear surface gravity waves

This manuscript describes the derivation of systems of equations for weakly nonlinear gravity waves in shallow water in the presence of constant vorticity. The derivation is based on a multi-layer generalization of the traditional columnar Ansatz. A perturbative development in a nonlinear parameter and a dispersive parameter allow us to obtain sets of equations, for the horizontal fluid velocity and the free surface, able to describe propagation of weakly nonlinear and dispersive surface waves moving in water with some prescribed initial constant vorticity. We have shown that vorticity plays a central role on the dispersive properties of the system. When it is weak, it acts as a correction in linear and nonlinear dispersive terms. When stronger, it can also influence the nondispersive behavior of the system. Explicit steady solutions of the system corresponding to zero, weak, normal or strong vorticity are obtained. They correspond to solitary waves. Evolution of the soliton celerity, amplitude and width for these four cases are discussed.

Equilibrium and scattering properties of a nonlocal three-soliton molecule in Bose–Einstein condensates with competing nonlinearities

We carry out numerical and variational investigation of equilibrium and scattering properties of a bright three-soliton molecule in Bose–Einstein condensates with competing local and nonlocal nonlinearities in one-dimensional geometry. Our model predicts that the degree of the nonlocality and the soliton phase may strongly affect the binding energy and the soliton width. We show that the interaction of three solitons depends on their separation distance and on their relative phase. The scattering properties of these composite nonlinear structures by Gaussian potential barrier are analyzed variationally and numerically. It is found that stable transmission and reflection where the molecular structure is preserved can occur only for a specific barrier height and soliton velocity.

Three-Dimensional Kadomtsev–Petviashvili Damped Forced Ion Acoustic Solitary Waves from Orbital Debris

Subcentimeter debris has been proven to cause significant damage to Earth-orbiting spacecraft sensors and subsystems; however, they are currently undetectable using ground-based radar and optical methods. Orbital debris will produce plasma density solitary waves, or solitons, due to their electrical charge, which propagate along the debris velocity vector, with amplitudes within the range of detectability by existing ground- and space-based sensors. Previously, using the damped forced Korteweg–de Vries equation, the orbital altitudes, latitudes, and velocities, where solitons can be produced by millimeter- to centimeter-sized debris, were identified in the presence of Landau damping and considering one spatial dimension. The soliton amplitude, width, speed, wavelength, and propagation distance were also modeled as a function of debris size and speed. Now, the full 3-D signature of orbital debris solitons is simulated using the damped forced Kadomtsev–Petviashvili equation. Transverse solitonic perturbations extend across the width of the debris, with predictable amplitudes and speeds that can be approximated by the 1-D damped forced Korteweg–de Vries equation at the transverse soliton location. The transverse perturbations form soliton rings that advance ahead of the debris in the 3-D simulations, allowing for additional opportunity for detection. The presented 3-D soliton predictions will facilitate design of future detection methods. Orbital debris solitons would enable the first collision-free mapping of the small debris population.

Exact soliton solutions in anisotropic ferromagnetic wires with Dzyaloshinskii–Moriya interaction* *Project supported by the Science and Technology Project of Hebei Education Department, China (Grant No. ZD2015133), the National Natural Science Foundation of China (Grant Nos. 61774001 and 12075102), the Natural Science Foundation of Hebei Province of China (Grant No. F2019202141), and the Program of State Key Laboratory of Quantum Optics

We theoretically investigate the exact soliton solutions of anisotropic ferromagnetic wires with Dzyaloshinskii–Moriya interaction. For example, we give the bright and black soliton solutions. From these results we find that the Dzyaloshinskii–Moriya interaction affects the existence region of soliton, spin-wave transport, and soliton dynamic properties. As the Dzyaloshinskii–Moriya interaction grows, the soliton width is widened, which provides a way to control the soliton dynamics.

Study of Dust-Acoustic Multisoliton Interactions in Strongly Coupled Dusty Plasmas

The effect of the structure parameter on the compressibility of dust grains and soliton behavior in a dusty plasma system consisting of Maxwellian electrons, ions, and dust grains charged with a negative charge has been studied. In the theoretical study, a reductive perturbation technique was used to derive the Korteweg-de Vries (KdV) equation and employ the Hirota bilinear method to obtain multisoliton solution. It is found that coupling and structure parameters have a clear effect on the compressibility. These changes in the compressibility affected the amplitude and width of interactive solitons, in addition to the phase shifts resulting from the interaction. These results can be used to understand the behavior of solitary waves that occur in various natural and laboratory plasma environments with dust impurity situations.