Slow Solitons Research Articles

Elastic overtaking collisions of large-amplitude ion-acoustic solitons

Overtaking collisions of large-amplitude solitons are investigated via fluid simulations for a plasma consisting of cold ions and Boltzmann-distributed electrons. To achieve this, a new fluid simulation code is presented. In addition, a novel approach to construct soliton initial conditions is developed. Using these ideas, initial conditions are combined that allows the simulation of overtaking collisions. It is shown that, in the small-amplitude regime, simulation results agree well with the two-soliton solution obtained from reductive perturbation theory. Interestingly, in the large amplitude regime, both the slow and fast solitons re-emerge after the collision with no significant change, showing that the collisions remain elastic. A comparison between reductive perturbation analysis and the simulations show that the only significant effect of higher order nonlinearities on overtaking collisions is a reduction in the magnitude of the phase shifts of both solitons.

Effects of two-temperature electrons on the slow and fast modulation instability and envelope solitons in a fully relativistic plasma

Effects of two-temperature electrons on the slow and fast modulation instability and envelope solitons in a fully relativistic plasma

A Mechanism for Large-Amplitude Parallel Electrostatic Waves Observed at the Magnetopause

Large-amplitude electrostatic waves propagating parallel to the background magnetic field have been observed at the Earth’s magnetopause by the Magnetospheric Multiscale (MMS) spacecraft. These waves are observed in the region where there is an intermixing of magnetosheath and magnetospheric plasmas. The plasma in the intermixing region is modeled as a five-component plasma consisting of three types of electrons, namely, two counterstreaming hot electron beams and cold electrons, and two types of ions, namely, cold background protons and a hot proton beam. Sagdeev pseudo-potential technique is used to study the parallel propagating nonlinear electrostatic solitary structures. The model predicts four types of modes, namely, slow ion-acoustic mode, fast ion-acoustic mode, slow electron-acoustic mode and fast electron-acoustic modes. Except the fast ion-acoustic mode, all other modes support solitons. Whereas slow ion-acoustic solitons have positive potentials, both slow and fast electron-acoustic solitons have negative potentials. For the case of 4% cold electron density, the slow ion-acoustic solitons have electric field ∼(40–120) mV m−1. The fast Fourier transforms (FFT) of slow ion-acoustic solitons produce broadband frequency spectra having peaks between ∼100 Hz to 1000 Hz. These theoretical predictions are in good agreement with the observations. The slow and fast electron-acoustic solitons could be relevant in explaining the low-intensity high (>1 kHz) frequency waves which are also observed at the same time.

Frequency combs with multiple offsets in THz-rate microresonators.

Octave-wide frequency combs in microresonators are essential for self-referencing. However, it is difficult for the small-size and high-repetition-rate microresonators to achieve perfect soliton modelocking over the broad frequency range due to the detrimental impact of dispersion. Here we examine the stability of the soliton states consisting of one hundred modes in silicon-nitride microresonators with the one-THz free spectral range. We report the coexistence of fast and slow solitons in a narrow detuning range, which is surrounded on either side by the breather states. We decompose the breather combs into a sequence of sub-combs with different carrier-envelope offset frequencies. The large detuning breathers have a high frequency of oscillations associated with the perturbation extending across the whole microresonator. The small detuning breathers create oscillations localised on the soliton core and can undergo the period-doubling bifurcation, which triggers a sequence of intense sub-combs.

In solid physics equations, accurate and novel soliton wave structures for heating a single crystal of sodium fluoride

This paper analyzes the analytical and numerical solutions’ structure of the combined mKdV equation and KdV equation (mKdV+KdV equation) using the Khater II (Khat. II) method and three accurate B-spline numerical schemes. ExCBS, SBS and TQBS numerical schemes are the numerical systems used. The handled model describes many distinct phenomena such as wave propagation of bounded particles with a harmonic force in a one-dimensional nonlinear lattice, propagation of ion-acoustic waves of small amplitude without Landau damping in plasma physics, and propagation of thermal pulse through a single sodium fluoride crystal in solid physics. Numerous examples show the relationship between quick and slow soliton, which generates phase shift. This phase shift is shown in a contour map to show the modest and colossal energy density along the path of fast and slow colliding solitons. Calculating the difference between analytical and numerical solutions shows whether they match spline-connected and distribution graphs.

Thickness-dependent slow light gap solitons in three-dimensional coupled photonic crystal waveguides.

The thickness-dependent multimodal nature of three-dimensional (3D) coupled photonic crystal waveguides is investigated with the aim of realizing a medium for controlled optical gap soliton formation in the slow light regime. In the linear case, spectral properties of the modes (dispersion diagrams), location of the gap regions versus the thickness of the 3D photonic crystal, and the near-field distributions at frequencies in the slow light region are analyzed using a full-wave electromagnetic solver. In the nonlinear regime (Kerr-type nonlinearity), we infer an existence of crystal-thickness-dependent temporal solitons with stable pulse envelope and use the solitonic pulses for driving quantum transitions in localized quantum systems within the photonic crystal waveguide. The results may be useful for applications in optical communications, multiplexing systems, nonlinear physics, and ultrafast spectroscopy.

Quantum squeezing of slow-light dark solitons via electromagnetically induced transparency

We consider the quantum effect of slow light dark soliton (SLDS) in a cold atomic gas with defocuing Kerr nonlinearity via electromagnetically induced transparency (EIT). We calculate the quantum fluctuations of the SLDS by solving the relevant non-Hermitian eigenvalue problem describing the quantum fluctuations, and find that only one zero mode is allowed. This is different from the quantum fluctuations of bright solitons, where two independent zero modes occur. We rigorously prove that the eigenmodes, which consist of continuous modes and the zero mode, are bi-orthogonal and constitute a complete bi-orthonormalized basis, useful for the calculation on the quantum fluctuations of the SLDS. We demonstrate that, due to the large Kerr nonlinearity contributed from the EIT effect, a significant quantum squeezing of the SLDS can be realized; the squeezing efficiency can be manipulated by the Kerr nonlinearity and the soliton's amplitude, which can be much higher than that of bright solitons. Our work contributes to efforts for developing quantum nonlinear optics and non-Hermitian Physics, and for possible applications in quantum information processing and precision measurements.

Large-amplitude electrostatic fluctuations at the Earth’s magnetopause with a vortex-like distribution of hot electrons

Large-amplitude electrostatic solitary waves (ESWs) associated with asymmetric magnetic reconnection at the Earth’s magnetopause are studied in a four-component plasma composed of a mixture of the magnetosheath and magnetosphere plasma of a cold, warm and hot electron populations, and background ions. The species are modeled as adiabatic fluids except for the hot electrons which have a kinetic vortex-like velocity distribution. The hybrid model uses the Sagdeev pseudopotential technique to study the arbitrary amplitude ion- and electron-acoustic solitons and double layers. The numerical computations reveal that for the parameters corresponding to magnetosphere side of the ion diffusion region, only slow electron-acoustic solitons and double layer can exist. On the magnetosheath side of the ion diffusion region, only the electron-acoustic/beam solitons can exist. The electric field amplitude of the electrostatic solitary waves (ESWs) predicted by our model are consistent with the Magnetospheric Multiscale (MMS) observations.

Ambiplasma separation into matter and antimatter by a train of baryon-acoustic solitons in the problem of the baryon asymmetry of the Universe

Longitudinal electrostatic baryon-acoustic waves have been studied systematically which can propagate in the uniform thermodynamically-nonequilibrium unmagnetized ambiplasma. The research was carried out in the frames of the linear theory and nonlinear theory according to the method of Sagdeev's pseudopotential. Two types of the periodic waves with in-phase (slow wave) and antiphase oscillations (fast wave) of protons and antiprotons were specified. The unknown before possibility of the existence of super-nonlinear waves in ambiplasma was shown for the first time. Fast and slow solitons were specified also. Wave profiles were calculated for all types of waves, they include flux profiles in the laboratory frame.Average proton and antiproton fluxes were calculated for the period of oscillations in the waves. It was shown that periodic trains of fast solitons could direct flows of protons and antiprotons in the opposite directions. This fact can be provided as a possible explanation of the baryon asymmetry of the modern Universe.

Slow and fast modulation instability and envelope solitons of ion-acoustic wave in electron–ion–positron plasma having ion stream and superthermal electrons

Slow and fast modulation instability and envelope soliton of ion-acoustic wave (IAW) are studied in an electron–ion–positron plasma when the ions are warm and have constant stream velocity, positrons are isothermal and electrons are superthermal. The non-linear Schrodinger (NLS) equation has been derived using the Fried and Ichikawa method and the solution of envelope soliton is obtained. It is seen that IAW propagates with two modes (slow and fast) in the presence of an ion stream in the plasma which results in slow and fast modulation instability of the wave. The stability criteria for slow mode (SM) and fast mode (FM) of the wave are established and studied graphically for different values of the ion temperature, positron density, positron temperature and kappa factor of electrons. The bright envelope soliton and dark envelope soliton of SM and FMs of the wave in electron–ion–positron plasma are also studied. The solution of rogue waves (RWs) is obtained from the NLS equation and the nature of RWs of the SM and FM of the wave is discussed graphically. Our results are new and no author has reported this kind of results of slow and fast modulation instability of IAW till now.

How can slow plasma electron holes exist?

One-dimensional analysis is presented of solitary positive potential plasma structures whose velocity lies within the range of ion distribution velocities that are strongly populated: "slow" electron holes. It is shown that to avoid the self-acceleration of the hole velocity away from ion velocities it must lie within a local minimum in the ion velocity distribution. Quantitative criteria for the existence of stable equilibria are obtained. The background ion distributions required are generally stable to ion-ion modes unless the electron temperature is much higher than the ion temperature. Since slow positive potential solitons are shown not to be possible without a significant contribution from trapped electrons, it seems highly likely that such observed slow potential structures are indeed electron holes.

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.

Large amplitude slow ion-acoustic solitons, supersolitons, and double layers in a warm negative ion plasma with superthermal electrons

The pseudopotential approach is used to investigate the ion thermal and electron superthermal effects on the slow mode solitary wave propagation characteristics in a negative ion plasma, comprising warm positive and negative ions and kappa-distributed electrons. The Sagdeev pseudopotential for the plasma model is derived and analyzed in a systematic way. While it is well known that a negative ion plasma supports the propagation of the fast mode normal solitons, it is found that it supports, in addition to the slow mode normal solitons, the propagation of the slow mode supersolitons and double layers for high values of the negative ion density. The double layers occur as the lower limit to the supersoliton existence range and as the limiting factor for the propagation of normal solitons. When the relative temperature of the two ion species decreases, it is found that the Mach number range supporting the propagation of the nonlinear structures reduces, while the amplitudes of solitons and supersolitons decrease, and these effects are enhanced by the superthermal behavior of the electrons. The amplitudes of the double layers increase with a decrease in the relative temperature of the two ion species but decrease with an increase in the electron superthermality.

A new class of Ion-acoustic solitons that can exist below critical Mach number

It is commonly believed that ion-acoustic solitons can only exist above the critical Mach number in a plasma system. A new class of ion-acoustic solitons that can exist below the critical Mach number is reported for the first time in a three-component plasma consisting of hot Maxwellian electrons, and two counterstreaming ion beams. The analysis is based on the Sagdeev pseudopotential technique, and considers a simple case of two counterstreaming proton beams with equal density and streaming velocity. Linear stability analysis shows that the slow ion-acoustic modes become unstable due to ion beam instability when the beam velocity normalized with the ion acoustic speed, U0, is in the range of 0.55 ≤ U0 ≤ 1.14. It is shown that when the normalized streaming velocity is below or at a threshold value, Uth = 1.14, only the regular solitons having Mach numbers greater than critical Mach number can exist. However, when the streaming velocity exceeds the threshold value (all modes are stable), both regular and the new class of ion-acoustic solitons can exist. A special case of unequal ion densities and unequal streaming velocities of the counterstreaming beams is considered in , and similar effects are found. Hence, the new class of slow ion-acoustic solitons can exist in the parametric regime where the system is stable to counterstreaming ion beams instability. The results could be useful in the interpretation of slow electrostatic solitary waves (ESWs) observed in the magnetosphere.

Kadomtsev-Petviashvili equation for magnetosonic waves in Hall plasmas and soliton stability

In this article we study nonlinear waves in Hall plasmas. We consider magnetosonic waves propagating at the angles with respect to the equilibrium magnetic field that are not close to either 0 or π/2. Using the reductive perturbation method we derive the three-dimensional Kadomtsev-Petviashvili (KP) equation. We use the KP equation to show that both fast and slow magnetosonic solitons are unstable with respect to transverse perturbations. We confront our results with the investigation of soliton stability in anisotropic media using the study of soliton self-refraction.

A new approach to analysis of dust-acoustic solitons with a self-consistent charge of dust particles

A new technique of analysis of dust-acoustic solitons based on an hydrodynamic model of dusty plasma with self-consistent charge of dust particles is developed. An advantage of the proposed approach is the use of only elementary functions. Charge fluctuations of dust particles inside the soliton as well as profiles of its potential and densities are calculated. The main characteristics of solitons are calculated in a wide range of plasma parameters. The conditions for the existence of extremely slow solitons are found. The calculations are performed for hydrogen, helium and argon plasmas.

Three coupled slow temporal vector optical solitons in a cold seven-level atomic system

A theoretical scheme is proposed to investigate the formation of three coupled slow temporal vector optical solitons in a lifetime-broadened seven-state atomic medium. We demonstrate that the three polarized components of a low intensity linear-polarized pulsed probe field can evolve into three coupled slow temporal vector optical solitons due to the fact that group-velocity dispersion can be well compensated by the self- and cross-phase-modulation effects. Moreover, this atomic system could support the existence of various types of three coupled slow temporal vector solitons, such as bright–bright–bright, bright–dark–bright, dark–dark–dark, and bright–dark–dark vector solitons.

Existence domain of electrostatic solitary waves in the lunar wake

Electrostatic solitary waves (ESWs) and double layers are explored in a four-component plasma consisting of hot protons, hot heavier ions (He++), electron beam, and suprathermal electrons having κ-distribution using the Sagdeev pseudopotential method. Three modes exist: slow and fast ion-acoustic modes and electron-acoustic mode. The occurrence of ESWs and their existence domain as a function of various plasma parameters, such as the number densities of ions and electron beam, the spectral index, κ, the electron beam velocity, the temperatures of ions, and electron beam, are analyzed. It is observed that both the slow and fast ion-acoustic modes support both positive and negative potential solitons as well as their coexistence. Further, they support a “forbidden gap,” the region in which the soliton ceases to propagate. In addition, slow ion-acoustic solitons support the existence of both positive and negative potential double layers. The electron-acoustic mode is only found to support negative potential solitons for parameters relevant to the lunar wake plasma. Fast Fourier transform of a soliton electric field produces a broadband frequency spectrum. It is suggested that all three soliton types taken together can provide a good explanation for the observed electrostatic waves in the lunar wake.

The effect of a warm electron beam on slow electron-acoustic solitons

The effects of the inclusion of finite drift speed of a warm electron component on the existence of arbitrary amplitude slow electron-acoustic solitons are investigated in a model with ions and cool, warm, and hot electrons. All plasma species are treated as adiabatic fluids. For fixed densities of the cool, warm, and hot electrons, the admissible Mach number ranges of the supported negative potential solitons are found to widen with increasing warm electron beam speed, up to a maximum value of vdbwo = 0.7. Beyond this maximum value, the soliton Mach number ranges become narrower and vanish completely at vdbwo = 1.084 where a switch to positive polarity solitons occurs. For a fixed value of the drift speed of the warm electrons, the cool electron density value at which the switch to positive polarity soliton occurs is the lowest when there is no streaming of the warm electrons but increases with increasing drift speed.

Electromagnetically induced transparency and nonlinear pulse propagation in a combined tripod and Λ atom-light coupling scheme

We consider propagation of a probe pulse in an atomic medium characterized by a combined tripod and Lambda (Λ) atom-light coupling scheme. The scheme involves three atomic ground states coupled to two excited states by five light fields. It is demonstrated that dark states can be formed for such an atom-light coupling. This is essential for formation of the electromagnetically induced transparency (EIT) and slow light. In the limiting cases the scheme reduces to conventional Λ- or N-type atom-light couplings providing the EIT or absorption, respectively. Thus, the atomic system can experience a transition from the EIT to the absorption by changing the amplitudes or phases of control lasers. Subsequently the scheme is employed to analyze the nonlinear pulse propagation using the coupled Maxwell–Bloch equations. It is shown that a generation of stable slow light optical solitons is possible in such a five-level combined tripod and Λ atomic system.