Formation Of Envelope Solitons Research Articles

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.

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.

Nonlinear interaction of intense laser beam with dense plasma

We studied the nonlinear evolution of an amplitude-modulated envelop soliton formed in a dense plasma when a laser beam interacts with it. The employment of our newly developed technique, homotopy-assisted symbolic simulation, has been instrumental in the study of the nature and formation of envelope solitons and their dependence on various parameters. The different orders of homotopy perturbation generate a convergent series solution for such nonlinear coupled partial differential equations (PDE). Our technique bypasses the rigorous analytical derivation of coupled PDE without a loss of information. The methodology is very novel and holds promise for application in models that explain experimental observations. The results will be beneficial in interpreting various dense laser plasma interactions.

Envelope solitons and rogue waves in Jupiter's magnetosphere

Considering a system of positively charged different sizes of dust grains which interacts with streaming electrons and ions, modulational instability (MI) together with the formation of envelope solitons and rogue waves are studied in Jupiter's middle magnetosphere. A nonlinear Schrödinger equation (NLSE) is derived and three distinct wave modes are observed among which the slowest mode is significantly affected by power law dust size distribution (DSD). For this mode, DSD enhances the MI growth rate in the unstable domain. The effects of densities of streaming electron and ion beams on the instability and different characteristics of the envelope solitons are investigated. How the number densities of electron and ion beams influence the spatiotemporal evolution of the associated rogue waves are also discussed.

Envelope solitons in three-component degenerate relativistic quantum plasmas

The criteria for the formation of envelope solitons and their basic features in a three-component degenerate relativistic quantum plasma (DRQP) system (containing relativistically degenerate electrons, non-degenerate inertial light nuclei, and stationary heavy nuclei) are theoretically investigated. The nonlinear Schrödinger equation is derived by employing the multi-scale perturbation technique. The envelope solitons are found to be associated with the modified ion-acoustic waves in which the inertia (restoring force) is provided by the mass density of light nuclei (degenerate pressure of cold electrons). The basic features of these envelope solitons, which are found to formed in such a DRQP system, and their modulational instability criteria (on the basis of the plasma parameters associated with the degenerate pressure of electrons, number densities of degenerate electrons, inertial light nuclei, and stationary heavy nuclei) are identified. The numerical simulations are also performed to confirm the stability of the envelope solitons predicted here by analytical analysis.

Modulation Instability of Ion-Acoustic Waves in Plasma with Nonthermal Electrons

Modulational instability of ion-acoustic waves has been theoretically investigated in an unmagnetized collisionless plasma with nonthermal electrons, Boltzmann positrons, and warm positive ions. To describe the nonlinear evolution of the wave amplitude a nonlinear Schrödinger (NLS) equation has been derived by using multiple scale perturbation technique. The nonthermal parameter, positron concentration, and ion temperature are shown to play significant role in the modulational instability of ion-acoustic waves and the formation of envelope solitons.

Nonlinear interaction of intense electromagnetic waves with a magnetoactive electron-positron-ion plasma

The nonlinear coupling between circularly polarized electromagnetic (CPEM) waves and acoustic-like waves in a magnetoactive electron-positron-ion (e-p-i) plasma is studied, taking into account the relativistic motion of electrons and positrons. The possibility of modulational instability and its growth rate as well as the envelope soliton formation and its characteristics in such plasmas are investigated. It is found that the growth rate of modulation instability increases in the case that ωc/ω<1 (ωc and ω are the electron gyrofrequency and the CPEM wave frequency, respectively) and decreases in the case that ωc/ω>1. It is also shown that in a magnetoactive e-p-i plasma, the width of bright soliton increases/decreases in case of (ωc/ω)<1/(ωc/ω)>1 by increasing the magnetic field strength.

Mechanisms of Gap Solitons Formation in Periodic Ferromagnetic Structures

The features of envelope soliton formation in one-dimensional periodic ferromagnetic structure were considered. The model based on the coupled nonlinear Schrodinger equations was used for investigation. The parameter space showing the region in which solitons similar to the Bragg solitons with di erent features can form was calculated. The mechanisms of the formation of the solitons localized on the limited length of the structure were considered.

On the formation of envelope solitons with tube ended by spherical beads

In this paper it is suggested the possibility of using a simple device to explore the propagation of short transverse perturbations in specimens of three linearly aligned elements (bead, tube and bead). By using time signal analysis and frequency spectroscopy some properties of the transmitted wave packets are experimentally analyzed in the acoustic domain. It is clearly demonstrated that the shape and the velocity of propagation of the waves do not change with distance. The amplitude may vary depending on the dissipation effect. These properties allow us to identify the wave packets as “envelope solitons”. The influence of the elasticity of these materials composing the beads and the tube on the generation of envelope solitons is also investigated.

Formation of envelope solitons of spin-wave packets propagating in thin-film magnon crystals

The formation of light envelope solitons has been experimentally observed under the pulsed excitation and propagation of radio-frequency spin-wave packets in a magnon crystal, a periodic magnetic film structure. The magnon crystal has been fabricated from a thin single-crystal yttrium iron garnet (YIG) film. The envelope solitons have been excited at frequencies corresponding to the edges of the Bragg-resonance-induced band gaps of the spin-wave spectrum of the magnon crystal. A theoretical explanation of the observed phenomenon has been proposed with the use of the numerical simulation of the formation of solitons based on the nonlinear Schrodinger equation.

Formation of envelope solitons from parametrically amplified and conjugated spin wave pulses

Formation of dipolar spin wave envelope solitons from input pulses parametrically amplified by microwave pumping has been investigated experimentally in an axially magnetized yttrium–iron–garnet (YIG) film waveguide by means of the space- and time-resolved Brillouin light scattering technique. The interaction of a linear input spin wave packet with double-frequency microwave pumping leads to the formation of two parametrically amplified contrapropagating wave packets: forward and phase-conjugated reversed. It was found that both forward and reversed packets immediately after the interaction with pumping increase their lengths almost two times compared to the length of the input packet. In the course of further propagation both wave packets demonstrate a significant compression in length (up to 2.5 times) which depends on the power of the input signal and is a clear signature of envelope soliton formation.

Nonlinear dynamics of upper-hybrid waves in dusty magnetoplasmas

The nonlinear propagation of upper-hybrid waves in a magnetized dusty plasma is considered. Several sets of Zakharov-like coupled equations are derived. They exhibit the nonlinear coupling between the high-frequency waves and various low-frequency electrostatic dusty plasma fluctuations. These nonlinear mode coupling equations are needed in forthcoming studies of modulational instabilities, envelope soliton formation, and wave collapse in dusty magnetoplasmas.

Modeling of nonlinear processes on magnetostatic waves in coupled ferromagnetic structures

System of nonlinear equations is obtained for the direct—volume—magnetostatic waves envelope solitons propagation in the coupling two—films ferromagnetic structure. Some features of soliton formation arising are considered in the framework of the numerical modeling at various structure parameters. The influence of the main structure parameters, pulse frequency and the dissipation on the process of the magnetostatic waves envelope soliton formation is examined.

Brillouin light-scattering observation of the nonlinear spin-wave decay in yttrium iron garnet thin films

The direct observation of nonlinear spin-wave decay in thin yttrium iron garnet (YIG) films is reported. The second-order parametric spin waves were excited by a series of nonlinear magnetostatic backward volume wave (MSBVW) pulses propagated in a microstrip structure at 5 GHz. Brillouin light-scattering techniques were used to detect spin waves in the YIG at a point along the propagation path. Data were obtained as a function of the input pulse duty cycle and peak power level. These data yielded the decay rate ${\ensuremath{\eta}}_{\mathrm{eff}}$ for the parametric spin waves vs input power ${P}_{\mathrm{in}}.$ This ${\ensuremath{\eta}}_{\mathrm{eff}}$ was equal to the usual spin-wave relaxation rate at low power, but decreased rapidly with increasing ${P}_{\mathrm{in}}.$ As ${P}_{\mathrm{in}}$ approached the threshold power for complete MSBVW soliton formation at the observation point, ${\ensuremath{\eta}}_{\mathrm{eff}}$ leveled off to a relatively constant value that was about a factor of 5--10 smaller than the low power value. The initial decrease in ${\ensuremath{\eta}}_{\mathrm{eff}}$ with power is due to the compensation of the usual spin-wave decay by the simultaneous parametric pumping of the spin waves by Suhl processes. The leveling off in ${\ensuremath{\eta}}_{\mathrm{eff}}$ at the soliton threshold is due to the spin-wave shedding that is needed to maintain order one eigenmode soliton propagation at high input power levels. These experiments demonstrate the reduction in the spin-wave decay rate with power below the threshold for spin-wave instability. This reduction is a key element in spin-wave instability theory that has never been observed directly. The data also demonstrate the enhanced production of parametric spin waves that accompanies microwave magnetic envelope soliton formation.

Stimulated scattering of high-power radio waves in multi-component collisional plasmas

Abstract The nonlinear coupling of intense radio waves with the low-frequency electrostatic perturbations of multi-component collisional plasmas is considered. Assuming the presence of two distinct groups of electrons and singly charged ions, we obtain equations for the radio wave sidebands and plasma slow motions that are driven by the combined effects of the radiation pressure and the differential Joule heating of the electrons. The mode coupling equations are useful for studying various types of stimulated scattering instabilities and envelope soliton formation. The relevance of our investigation to the simultaneous generation of density and temperature fluctuations by high-power radio waves is pointed out.

Envelope soliton formation length in magnetic films (abstract)

Envelope solitons of magnetostatic waves (MSW) propagating in magnetic films have recently become an object of intensive experimental and theoretical study.12 It has been shown experimentally1 that the amplitude of a fully formed envelope soliton in a weakly dissipative magnetic film decreases with propagation distance (or delay time) twice as fast as the amplitude of a sinusoidal wave in the same film. In the present paper, we report a detailed study of the process of envelope soliton formation for MSW in a high-quality, yttrium iron garnet (YIG) film. As a result of this study, we propose to define the soliton formation length L as a distance at which the doubled “solitonic” dissipation of the propagating pulse starts to manifest itself. Figure 1 shows the evolution of an input rectangular pulse (duration T=12 ns, power 1.1 W, carrier frequency 5.6 GHz of backward volume MSW propagating in a YIG film [thickness 14.6 μm, ferromagnetic resonance (FMR) linewidth 2ΔH=0.8 Oe] as a function of the propagation time Tp=Lp/Vg, where Lp is the propagation distance, and Vg=6.67×106 cm/s is the group velocity. It is clear that linear (in logarithmic scale) decrease of the output pulse amplitude starts at propagation time Tp=45 ns corresponding to Lp=Lf=0.3 cm. Our measurements have shown that the soliton formation distance Lf is practically independent of the power of the input rectangular pulse (in the interval 0.5 W<Pin<1.3 W, corresponding to the formation of a single soliton), and is determined mainly by the input pulse duration T. It is interesting to compare the experimentally determined value of Lf to the value of dispersion length Lp, which is widely used in literature.3 For a rectangular input pulse (of duration T) we get LD=T2Vg3/π2|D|, where D=5×103 cm2/s is the wave dispersion. Calculation using Eq. (Equation 1) shows that for the conditions of our experiment LD=0.86 cm or roughly three times larger than Lf.

Thresholds of Envelope Soliton Formation for Dipole-Exchange Spin Waves in Yttrium-Iron Garnet Films

The power thresholds of spin wave envelope soliton formation from input rectangular radio-pulses of duration Tin a thin yttrium-iron garnet (YIG) film were studied experimentally. The measurements were done for strongly dispersive dipole-exchange spin waves in the vicinity of one of the dipole gaps in the spectrum of a film with strongly pinned surface spins. The observed threshold curve P th = f (1/T 2 ) is non-monotonous and has a fine structure consisting of three minima corresponding to the formation of n = 1, 2, and 3 solitons. The observed shape of the threshold curve is explained by the theory of envelope soliton formation where dissipation in the medium is taken into account. The values and positions of the minima on the experimentally measured threshold curve are determined by the dissipation parameter Γ = γ ΔH which is proportional to the half-linewidth ΔH of ferromagnetic resonance in the experimental YIG film.

Thresholds of Envelope Soliton Formation in a Weakly Dissipative Medium.

Thresholds of envelope soliton formation from input rectangular pulses of amplitude $b$ and duration $T$ in a nonlinear dispersive medium with weak dissipation are calculated. The calculated threshold curve ${b}_{\mathrm{th}}^{2}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}f({1/T}^{2})$ has $n$ minima corresponding to the formation of $1,2,\dots{},n$ envelope solitons. The positions and magnitudes of these minima are determined by the dissipation parameter in the medium. The derived threshold formula provides a quantitative description of the threshold curve measured recently for spin wave envelope solitons in yttrium-iron-garnet films.

Thresholds of spin wave envelope soliton formation in magnetic films with dissipation (abstract)

The nonlinear mechanism responsible for the spin wave envelope soliton formation in magnetic films from input pulses of finite duration is the four-wave process with conservation law ω(k0)+ω(k0)=ω(k0+κ)+ω(k0−κ), κ≪k0. This process is also responsible for modulation instability of CW wave in a nonlinear dispersive medium and can only take place if the nonlinearity N and the dispersion D in the medium have opposite signs. In a dissipative medium this process has a finite amplitude threshold determined by the dissipation parameter γ and the effective ‘‘detuning’’ Δω proportional to the dispersion D and the square of the modulation wave number κ, ‖φ‖th2=[γ2+(Δω)2/4]/‖NΔω‖, hereafter referred to as Eq. (1), where ‖φ‖ is the dimensionless wave amplitude. For the process of modulational instability of a CW wave Δω=Dκ2. For the process of soliton formation from a finite input pulse (of the duration T) Δω=Dκ2n, where κn=(2n−1)π/vT, n is the number of solitons formed, and v is the group velocity of spin waves. Equation (1) gives a good description of the recent measurements of thresholds of spin wave envelope soliton formation in YIG films presented in Ref. . In particular, describes correctly the shape of the threshold curve, positions of threshold minima for the formation of one and two solitons, and explains the finite intercept on the threshold power dependence on the inverse square of the input pulse duration that was not explained in Ref. .

Influence of the carrier signal phase on the formation of "Dark" spin wave envelope solitons in magnetic films

A process of formation of "dark" spin wave envelope solitons in magnetic films is considered. It is shown that a 180/spl deg/ phase shift in the carrier frequency of an input rectangular negative radio-pulse is necessary to create a single "dark" envelope soliton. The input signal with no phase shift can create only a pair (or several pairs) of "dark" envelope solitons. A new interpretation of a recent experimental observation of "dark" spin wave envelope soliton formation in yttrium-iron garnet (YIG) films is given.