Soliton Width Research Articles

Circularly polarized dust Alfvén solitary waves in magnetized gravitative-radiative quantum dusty plasma

An effective single fluid quantum magnetohydrodynamic model is used for multicomponent dusty plasma composed of degenerate electrons, ions, and nondegenerate dust species for the investigation of nonlinear circularly polarized dust Alfvén waves in the presence of quantum corrected terms like Fermi and radiation pressures of electrons and ions as well as Jeans term that originates in a self-gravitating, dusty plasma. A set of Zakharovlike equations are derived and are used independently for soliton solutions, incorporating quantum terms and the Jeans term. Using the Sagdeev potential approach, it is observed that ordinary solitons may result in the absence of the Jeans term, whereas cusp solitons are obtained in the presence of the Jeans term. The variation of Sagdeev potential and its associated solitary structure for different parameters are discussed for both right and left handed circularly polarized dust Alfvén waves. It is also observed that increasing the values of the magnetic field and decreasing the dust mass enhance the width of the cusp soliton, while the amplitude remains the same. The modulational instability of the system in view of both quantum and Jeans terms is also looked into, and different conditions of stability and instability for both right and left handed circularly polarized quantum dust Alfvén waves are discussed.

Length-scale competition in the parametrically driven nonlinear Dirac equation with a spatially periodic force

Soliton dynamics in the damped and parametrically driven nonlinear Dirac equation, in 1 + 1 dimension with scalar–scalar self-interaction is analysed. The considered parametric force has the spatial period . A variational approach using collective coordinates for studying the time dependent response of the solitary waves to this parametric force is developed. The dynamical equations for the collective coordinates are also obtained by an alternative method, namely the method of moments. The soliton dynamics depends crucially on the competition between two length scales: the spatial period and the width of the soliton ls. For the soliton oscillates in an effective potential, while for it moves uniformly as a free particle. The transition between these two regimes occurs when is comparable to the soliton width. This match enhances the soliton instabilities so that even small values of the perturbation are enough to modify drastically the soliton shape and destroy it for long times.

Temporal behaviour of bright solitons in photorefractive crystals having both the linear and quadratic electro-optic effect

Abstract We investigate the characteristics of formation or time evolution of optical spatial solitons in novel photorefractive media having both the linear and quadratic electro-optic effect. We have derived a one dimensional time dependant wave propagation equation in biased photorefractive media having both the linear and quadratic electro-optic effect. The variation of soliton width with time is investigated for different values of peak intensity ratio and it is shown that these bright solitons can exist both in the quasi steady state and steady state regimes for high saturation values. Two distinct regimes of intensity ratio are identified where the soliton formation characteristics are different. Only steady state solitons are formed if the intensity ratio is small. Soliton characteristics like the initial soliton width, steady state soliton width, and quasi steady state soliton width are investigated for both regimes and found to depend on as varying functions of the intensity ratio. We also find that the individual magnitudes of the linear and quadratic electro-optic coefficients affect the temporal characteristics of formation of the solitons. Appropriate example has been taken for an illustration of our results.

Quantum dark solitons in the one-dimensional Bose gas

Dark and grey soliton-like states are shown to emerge from numerically constructed superpositions of translationally-invariant eigenstates of the interacting Bose gas in a toroidal trap. The exact quantum many-body dynamics reveals a density depression with superdiffusive spreading that is absent in the mean-field treatment of solitons. A simple theory based on finite-size bound states of holes with quantum-mechanical center-of-mass motion quantitatively explains the time-evolution of the superposition states and predicts quantum effects that could be observed in ultra-cold gas experiments. The soliton phase step is shown to be a key ingredient of an accurate finite size approximation, which enables us to compare the theory with numerical simulations. The fundamental soliton width, an invariant property of the quantum dark soliton, is shown to deviate from the Gross-Pitaevskii predictions in the interacting regime and vanishes in the Tonks-Girardeau limit.

Solitary dispersive Alfvén wave in a plasma composed of hot positrons, cold electrons and ions

The nonlinear solitary structure of the dispersive Alfvén wave in an three-component plasma with hot positron, cold electron and ion is studied from the multi-fluid theory. It is found that when the equilibrium number density ratio of ion to electron is finite, there only exists the super-Alfvén rarefactive solitons. The increase of the ion concentration or the speed of soliton will lead a deeper depletion of the electron number density. The width of soliton decreases with the increase of the speed of soliton and the ion concentration. When the equilibrium number density ratio of ion to electron is much less than unity, there are only sub-Alfvén rarefactive solitons. In the case, the larger speed of soliton or the smaller concentration of ions result the deeper depletion of the electron number density. The width of the soliton increases with the ion concentration and the speed of soliton. The results obtained may be related to the observations and experimental results in the electron positron plasma.

Dust Charging and Propagation of Dust-Acoustic Waves in a Multicomponent Thermal Dusty Plasma System

An analytical model is developed with the aim to investigate the propagation of dust-acoustic (DA) waves in a multicomponent thermal dusty plasma system including ion species as well. Dust particles are considered positively charged by electron and ion currents, thermionic and UV photo-ionic processes. The model is applied to laboratory plasma as well as Martian atmospheric plasma to explain the nature of dust potential variation as well as characteristics of DA propagation modes within the linear and nonlinear regimes for given plasma parameters. In the nonlinear regime, the KdV equation is derived, and the equation is seen to support the propagation of compressive solitons in laboratory plasma system and rarefactive solitons in the case of Martian atmospheric plasma. The inclusion of ion species in the system is seen to have an important role in determining the propagation speed, the amplitude, and the corresponding width of solitons. The thermionic work function W, photon yield factor Y, and low value of flux density of UV photon beam J do not have an appreciable impact on dispersion relation and DA soliton structures. On the contrary, noticeable changes occur in the case of the dust surface potential obtained in both laboratory and Martian plasmas.

Control on interaction of Airy-Gaussian beams in competing nonlinear medium

An investigation of control on the interaction of Airy-Gaussian beams (AiGBs) in cubic focusing and quintic defocusing competing nonlinear medium is performed by the split-step Fourier transform method. When the initial launch angle <i>v</i> is zero, two in-phase AiGBs attract each other and the breathing soliton with decaying period or soliton with invariant intensity can form in the case of weaker quintic defocusing nonlinearity. However, the interaction between two in-phase AiGBs under stronger quintic defocusing causes the average width of the breathing soliton to increase and even the beam bifurcation to occur, leading to the generation of soliton pairs. For the out-of-phase case, they repel each other, and the repulsive force increases monotonically with the increase of the quintic defocusing nonlinearity. When the initial launch angle for each of AiGBs is not zero, mutual attraction and repulsion can be exhibited during their interactions by adjusting the sign of <i>v </i> and the interval <i>d</i>. For the in-phase case, if <i>v</i> < 0 and <i>d</i> < 0 or <i>v</i> > 0 and <i>d</i> > 0, there are strong repulsive force and weak attraction between the two AiGBs, resulting in the formation of soliton pairs, and with the decrease of the interval, the attraction becomes greater. When the interval is small enough, the overlapping of the light field can make the nonlinear effect identical to the diffraction effect, the attraction between the two AiGBs increases, while the repulsion force is almost zero, and then a single breathing soliton can be generated in the center of the two AiGBs. If <i>v</i> < 0 and <i>d</i> > 0 (big enough) or <i>v</i> > 0 and <i>d</i> < 0, the constructive interference between two AiGBs causes the autofocusing beams first to be generated, then to repel each other, and the soliton pairs can form. For the out-of-phase case, if <i>v</i> < 0 and <i>d</i> < 0 or <i>v</i> > 0 and <i>d</i> > 0, the repulsion between the two AiGBs becomes bigger, and the repulsion increases with |<i>v</i>| monotonically. If <i>v</i> < 0 and <i>d</i> > 0 or <i>v</i> > 0 and <i>d</i> < 0, the elastic collision between the two AiGBs shows the phenomenon: first attracting and then repelling mutually. When both <i>v</i> and <i>d</i> are small enough, soliton pairs cannot form due to the unbalance between the strong diffraction effect and weaker nonlinear effect induced by the destructive interference.

Dust acoustic solitons in a dusty plasma with Cairns–Gurevich distributed ions

The problem of dust acoustic solitons is addressed in an unmagnetized collisionless dusty plasma with ions satisfying a Cairns–Gurevich distribution. A new type of density that describes, simultaneously, the evolution of the energetic ions and those trapped in the plasma potential well is outlined. Both highly and weakly nonlinear waves are investigated by deriving the Sagdeev potential for the large amplitude limit, and establishing the nonlinear partial differential equations (mK–dV equation) for the small but finite amplitude limit. It is shown that the effect of the nonthermal ion trapping on DA waves can be quite important. In particular, an increase of nonthermal character of ions following the Cairns–Gurevich distribution lead to an increase of the main quantities (amplitude and width) of dust acoustic solitons. Our investigation will be helpful in understanding the nonlinear DA waves in the presence of nonthermal trapped ions which may exist in space.

Interaction of solitons with impurities in anisotropic ferromagnetic chains

The interaction of bright solitons with impurities in the on-site anisotropy of a ferromagnetic chain is studied. This type of impurities leads to linear and nonlinear perturbing terms in the corresponding nonlinear Schrödinger equation. We have found static soliton-impurity bound states and considered the conditions for their formation. For large values of the anisotropy the character of the impurities is mainly linear. The interaction of propagating solitons with the impurities is also investigated. We have obtained that the solitons can be transmitted, trapped or reflected. The behavior depends on the soliton velocity and width, magnetic parameters and the impurity strength.

Quantum soliton evaporation

Quantum evaporation may occur in a variety of systems such as superfluids, Bose-Einstein condensates, and gravitational black holes (Hawking radiation). However, to date all predictions are based on semiclassical models, e.g., the Einstein equations and classical space-time metric for a black hole and only the fluctuations are quantized. Here we use a fully quantized dynamical equation, the quantum nonlinear Schr\odinger equation, to study the evolution of quantum solitons. As a result of quantum fluctuations in the center-of-mass position, the expectation value of the quantum soliton width increases and concomitantly evaporates through the emission of frequency-entangled photon pairs. The frequency of this emission decreases as the soliton evaporates due to the soliton spreading. In the final phase, the soliton mean field collapses irreversibly into a state with zero mean amplitude. These results may provide insight to quantum evaporation in other systems where a full quantum description is still to be developed and highlights that even classically stable systems may also be subject to quantum evaporation.

Probing non-locality of interactions in a Bose–Einstein condensate using solitons

We consider a Bose–Einstein condensate (BEC) with non-local inter-particle interactions. The local Gross–Pitaevskii (GP) equation is valid for the gas parameter , but for , the BEC is described by a modified GP equation (MGPE). We study the exact solutions of the MGPE describing bright and dark solitons. It turns out that the width of these non-local solitons has qualitatively similar behaviour as the modified healing length due to the non-local interactions of the MGPE. We also study the effect of the non-locality and gas parameter (ν) on the stability of the solitons using the Vakhitov–Kolokolov (VK) stability criterion. We show that these soliton solutions are stable according to the VK criterion. Further, the stability of these soliton solutions gets enhanced due to the non-locality of interactions.

Lax pair, binary Darboux transformations and dark-soliton interaction of a fifth-order defocusing nonlinear Schrödinger equation for the attosecond pulses in the optical fiber communication

ABSTRACT Under investigation in this paper is a fifth-order defocusing nonlinear Schrödinger equation for the attosecond pulses in the optical fiber communication. Lax pair, one/N-fold binary Darboux transformations and the limit forms of the one-fold binary Darboux transformation for such an equation are obtained. Based on one/N-fold binary Darboux transformations and the limit forms of the one-fold binary Darboux transformation, one- and N-dark soliton solutions are obtained. Soliton amplitude is not affected by the coefficients of the nonlinear-Schrödinger operator, Hirota operator, Lakshmanan-Porsezian-Daniel operator and quintic operator, but soliton velocity is linearly related to them. Overtaking interaction between the two solitons is illustrated. Parallel solitons are formed: soliton width and interval between the parallel solitons are decreased with the increasing value of each and every coefficient of the nonlinear-Schrödinger operator, Hirota operator, Lakshmanan-Porsezian-Daniel operator and quintic operator respectively. For the interactions among the three solitons, e.g. interaction among three overtaking solitons, and interaction between the parallel solitons and a single soliton are displayed. We find that the interactions between the two solitons and among the three solitons are elastic.

Spatial solitons supported by graphene/hexagonal boron nitride heterostructures

In this paper, we show how the diffraction of light beams is balanced by the nonlinearity of graphene/hexagonal boron nitride heterostructures, which discretely occurs in the very thin graphene layers, forming spatial solitons. We also discuss the effects of the layer number and the peak E-field amplitude on the soliton width.

Exciton-polariton soliton wavetrains in molecular crystals with dispersive long-range intermolecular interactions

The peculiar crystal structure of one-dimensional molecular solids originates from packing of an array of molecules in which intermolecular interactions are dominantly dispersive, including hydrogen-bond, van der Waals and London-type forces. These forces are usually relatively weaker than covalent and ionic bondings such that long-range intermolecular interactions should play important role in dispersion properties of molecular crystals such as polymers and biomolecular chain structures. In this work the effects of long but finite-range intermolecular interactions on single-exciton dispersion energy, and hence on characteristic parameters of periodic soliton trains associated with bound exciton-polariton states in one-dimensional molecular crystals interacting with an electromagnetic field, are investigated. Long-range interactions are shown to quantitatively modify the exciton-polariton soliton amplitudes, width and velocity as a result of shrinkage of the single-exciton energy spectrum. The soliton structures of interest are nonlinear wavetrains, consisting of periodically ordered single-pulse (i.e. bright) or single-kink (i.e. dark) solitons with equal separation between the constituent single-soliton modes. Periodic soliton structures are relevant and best suited for finite-size chain systems, where periodic boundary conditions rule the generation of nonlinear wave profiles. Generally they are of weaker nonlinearity compared to their single-soliton constituents as well established within the framework of their generation via the process of modulational instability

Universal isocontours for dissipative Kerr solitons.

Dissipative Kerr solitons can be generated within an existence region defined on a space of normalized pumping power versus cavity-pump detuning frequency. The contours of constant soliton power and constant pulse width in this region are studied through measurement and simulation. Such isocontours impart structure to the existence region and improve understanding of soliton locking and stabilization methods. As part of the study, dimensionless, closed-form expressions for soliton power and pulse width are developed (including Raman contributions). They provide isocontours in close agreement with those from the full simulation, and, as universal expressions, can simplify the estimation of soliton properties across a wide range of systems.

Analytical Solutions and Parametric Studies of the Schamel Equation for Two Different Ion-Acoustic Waves in Plasmas

A numerical investigation of the properties of two different ion-acoustic solitons has been performed by using analytical solutions of the Schamel equation. A new type of the analytical solution of the Schamel equation that describes soliton propagation with a negative phase velocity has been found for the first time. This new type of the solution has been applied to investigate the physical properties of two different plasmas and to understand the effect of nonextensivity and the effect of trapped electrons on ion-acoustic waves in a superthermal plasma. It is shown that the soliton amplitude and width depend on the nonextensivity parameter, superthermality of the electron distribution, and characteristic trapping parameter.

Fundamental solitons in the nonlinear fractional Schrödinger equation with a -symmetric potential

We address the existence and stability of fundamental solitons in a -symmetric Gaussian potential embedded into a material with fractional effects. Fundamental solitary waves with low power both in defocusing and focusing medium originate from the same eigenmode, and the smaller the Lévy index, the narrower the width of solitons. The linear stability analysis of fundamental solitons has been carried out in fractional dimension. -symmetric solitons are completely stable for a moderate Lévy index and gain/loss coefficient in a wide existence region.

Dark gap solitons in exciton-polariton condensates in a periodic potential.

We show that dark spatial gap solitons can occur inside the band gap of an exciton-polariton condensate (EPC) in a one-dimensional periodic potential. The energy dispersions of an EPC loaded into a periodic potential show a band-gap structure. Using the effective-mass model of the complex Gross-Pitaevskii equation with pump and dissipation in an EPC in a periodic potential, dark gap solitons are demonstrated near the minimum energy points of the band center and band edge of the first and second bands, respectively. The excitation energies of dark gap solitons are below these minimum points and fall into the band gap. The spatial width of a dark gap soliton becomes smaller as the pump power is increased.

Chirped bright and dark solitons of electric and magnetic coupled nonlinear field equations in negative-index metamaterials

The generalized coupled nonlinear Schrödinger equations govern the pulse propagation of electric and magnetic fields in negative index materials. Based on the F-function expansion method, Jacobian elliptic function solution and bright and dark soliton solutions are obtained. Dynamics behaviors of bright and dark solitons are studied. Bright and dark solitons exist both in the normal dispersion regimes. The amplitudes and widths of bright and dark solitons are decided by parameters SE, SH related to electric and magnetic self-steepening effects. The phase chirp of bright and dark soliton shifts along the positive time-axis with the increase of the propagation distance.

Generation of bright-dark soliton trains with a central wide dip in optical fibers

The nonlinear propagation dynamics of the dark soliton pulse with hyperbolic tangent profile in the anomalous dispersion regime of an optical fiber is investigated numerically. The corresponding temporal evolutions are provided for different integral or non-integral soliton order and loss perturbations. The results show that, irrespective of the integral or non-integral soliton order, with increase of distance, the width of the dark soliton broadens and more and more bright and dark pulses appear symmetrically on the two sides of the central black soliton. Correspondingly, bright-dark soliton trains with a central wide black soliton can gradually form. The higher the soliton order, the more the bright-dark pulses at the same distance. With increase of distance, the peak values of the bright pulses exhibit oscillation behavior. The loss perturbation only influences the evolutions slightly, which means that the generated soliton trains can resist loss perturbations to some extent. Moreover, this work provides us an alternative approach to generate bright-dark soliton trains by using the dark soliton pulse propagating in the anomalous dispersion regime of the passive optical fiber besides directly using the fiber laser.