Solitons In Arrays Research Articles

Stability of one-dimensional array solitons.

The array soliton stability in the discrete nonlinear Schrödinger equation with dispersion for periodic boundary conditions is studied. The linear growth rate dependence on the discrete wave number and soliton amplitude is calculated from the linearized eigenvalue problem using the variational method. In addition, the eigenvalue problem is solved numerically by shooting method and a good agreement with the analytical results is found. It is proved numerically that the results for the instability threshold for the circular array coincides with the quasicollapse threshold for the case of open arrays with initial pulses in a form of array solitons.

Towards thermodynamics of solitons: cooling

Recently it has been shown that pulse reshaping in a synchronously driven fibre ring resonator can give rise to the formation of a soliton array which may exist either in a `fluid' or `solid' state, called a soliton gas and soliton crystal, respectively. Here, we demonstrate in numerical simulations that a soliton gas can be cooled to a soliton crystal by a procedure analogous to evaporative cooling.

Impurity-induced stabilization of solitons in arrays of parametrically driven nonlinear oscillators

Chains of parametrically driven, damped pendula are known to support solitonlike clusters of in-phase motion which become unstable and seed spatiotemporal chaos for sufficiently large driving amplitudes. We show that the pinning of the soliton on a "long" impurity (a longer pendulum) expands dramatically its stability region, whereas "short" defects simply repel solitons producing an effective partition of the chain. We also show that defects may spontaneously nucleate solitons.

Lattice Soliton: Solution to the Davey-Stewartson Equation

A lattice soliton solution with doubly periodic structure in the x-y plane is constructed as the imbricate series of rational soliton solutions to the Davey-Stewartson equation, which seems doubly periodic arrays of the infinite rational solitons. The existence condition and some properties of the lattice soliton solution are also presented.

Signal amplification by means of cavity solitons in semiconductor microcavities

Cavity solitons were recently predicted in semiconductor microresonators grown with a vertical geometry. By exploiting a previously introduced model valid for both passive and active configurations of a multiple-quantum-well device, we studied the response in the time domain offered by such self-organized structures in the device, when a small modulated optical signal is applied. Using appropriate symmetry considerations, the (2+1)-dimensional problem is reduced to a tractable form, by means of a semianalytical method. We demonstrated that large differential-gain factors, competitive with those of other all-optical and some opto-electronic devices, are attainable, when the output signal is collected at the peak of the cavity soliton. This fact, in connection with the reconfigurability properties already established for cavity soliton arrays, allows to conceive different schemes for optical information handling: feasible arrangements for parallel amplification and for signal commutation are proposed.

Wandering and Bunching Instabilities of Steps Described By Nonlinear Evolution Equations

We study wandering and bunching instabilities of steps in a surface diffusion field with a direct electric field applied perpendicular to the steps. The drift of adatoms induced by the electric field modifies the surface diffusion length in the upper terrace and that in the lower terrace. This asymmetry causes wandering instability of an isolated step when the drift is opposite to the step motion. Near the critical point the time evolution of a step obeys the Kuramoto–Sivashinsky equation, which gives rise to spatiotemporal chaos. The asymmetry also causes bunching instability of an array of repulsive straight steps. The instability near the critical point is an amplification of density large wavelength. The step density after the instability obeys the Benney equation, which shows a stable array of solitons corresponding to the formation of stable bunches.

Spatial Structures in Semiconductor Devices

The basic physics of nonlinear optics in semiconductors is reviewed. Optical bistability due to increasing absorption and in a Kerr cavity is discussed, as are spatial solitons in a Kerr medium. These introduce recent research on spontaneous pattern formation and soliton-like structures in semiconductor cavity models. Applications to optical information processing are discussed, and simulations of a soliton array memory presented.

Soliton energy band for the six-fold degenerated CDW in the K2Pt(CN)4Br0.3·3.2H2O system

Abstract The formation of soliton bands in the quasi-one-dimensional mixed valence planer platinum compound K2Pt(CN)4Br0.3·3.2H2O (KCP) as a result of overlapping soliton wave functions is considered. A solitonic energy band dependence on temperature and the associated phonon modes of the soliton array are suggested to be responsible for the ESR linewidth broadening observed in this material for temperatures above 85 K.

Instability of solitons in an inhomogeneous array of optical fibers

The perturbation theory for an investigation of the stability of solitons in fiber array with a periodic change of a coupling constant is developed. The linear stability analysis is performed in an approximation of weak coupling within the framework of the system of dispersive discrete nonlinear Schr\"odinger equations. It is shown that the propagation of a soliton array in such a continuous-discrete system is unstable. The maximum of the growth rate of modulation instability is evaluated. Analyzing the mode structure of the corresponding eigenvalue problem in the vicinity of the threshold of instability it is found that in the system under consideration acoustical and optical unstable modes exist. Numerical calculations confirm the analytical results.

HARMONIC SUPERPOSITIONS OF NONEXTREMAL p-BRANES

The plot of allowed p and D values for p-brane solitons in D-dimensional supergravity is the same whether the solitons are extremal or nonextremal. One of the useful tools for relating different points on the plot is vertical dimensional reduction, which is possible if periodic arrays of p-brane solitons can be constructed. This is straightforward for extremal p-branes, since the no-force condition allows arbitrary multicenter solutions to be constructed in terms of a general harmonic function on the transverse space. This has also been shown to be possible in the special case of nonextremal black holes in D=4 arrayed along an axis. In this paper, we extend previous results to include multiscalar black holes, and dyonic black holes. We also consider their oxidation to higher dimensions, discuss general procedures for constructing the solutions and study their symmetries.

Suppression of soliton jitter by a copropagating support structure

A new way to suppress the soliton’s jitter in long-haul optical communication systems is proposed that does not use in-line filters. Parallel to the information-carrier soliton stream, a periodic stiff array (consisting of bright or dark solitons) is launched in another mode, which may be either an orthogonal polarization or, more realistically, another wavelength. This support array induces, through the cross-phase modulation, an effective potential pinning of the signal solitons. Most promising is the scheme in which the support structure is an array of dark solitons (while the information is carried by the bright ones). In the analytical part of the work we derive a Langevin equation for the information soliton in the presence of the induced potential and of a random force representing the jitter, for both cases when the support channel has anomalous or normal dispersion. Next, we derive the corresponding Fokker–Planck equation. A solution to this equation explicitly demonstrates a strong suppression of the jitter in comparison with the Gordon–Haus limit. To check this mechanism directly we perform numerical simulations of the coupled nonlinear Schrodinger equations for the information and support channels, including the jitter-generating random perturbations acting in both of them. The simulations demonstrate that, while in the absence of the support structure the soliton’s jitter is growing in accord with the Gordon–Haus law, the support structure strongly suppresses the jitter, as is predicted by the analysis.

Instability of continuous waves and rotating solitons in waveguide arrays

The effect of a nonvanishing transverse wave vector on the stability of continuous waves and temporal solitons which propagate in an array of nonlinear optical waveguides is studied both analytically and numerically. We derive analytical expressions for the domain of existence as well as the gain of modulational instability of moving continuous waves. Because the transverse wave vector controls the ``discrete diffraction'' the stability behavior critically depends on this quantity. By employing the perturbation theory near neutrally stable modes it is shown that there are two different scenarios for the evolution of modulationally unstable soliton arrays. The transverse wave vector of the unstable solution determines which kind of instability develops. Numerical calculations confirm the analytical results.

Excitation and dynamics of pulses in coupled fiber arrays

We consider a system of nearest neighbor linearly coupled nonlinear Schrödinger equations. The system models a coupled array of optical fibers in the anomalous dispersion regime. In the infinite array case, a sharp power threshold for the excitation of a coupled array soliton (nonlinear ground state) is found. For the periodic array (ring geometry), a soliton is excited for arbitrary values of the power. Coupled array solitons are nonlinearly dynamically stable. As the power increases, the coupled array solitons become increasingly peaked in amplitude, localized on the lattice as well as temporally compressed. As the power tends to infinity, a rescaled limit of the ground state converges to a pure one-soliton. The results provide a mathematical theory for the observations of previous investigators made by computer simulations.

SOLITON SOLUTIONS OF PERIURBED BURGERS-KdV EQUATION

In this paper , we have studied a perturbed Burgers-Korteweg-de Vries equation ut+uux+βuxxx=εuxx,|ε|?1, Under first order approximation and travelling wave case, the direct perturba-tion method to find the general solution is established. By means of the single soliton solution of the zeroth order equation we have obtained the general soliton solution of the first order equation. It con-tains many diferent soliton solutions and any one of them describes an array of solitons in semi-infinite space. The analyses show that the dissipation e makes the bright soliton the lower and narrower and the dark soliton the shallower and narrower than unperturbed KdV soliton.

Collision of Two Real Dark Spatial Solitons

We study the collision of two dark spatial solitons immersed in their own finite background beams. We show that real spatial solitons can cross each other only for certain combinations of the collision angle and the intensities of the beams. Otherwise, the collision pattern evolves into an array of quasi-dark solitons due to the internal gain caused by the modulation instability effect.

A devil's staircase in the Zeeman response of the 1D half-filled adiabatic Holstein model

The magnetization of the half-filled 1D adiabatic Holstein model in a magnetic field is investigated at 0 K. It has been proven elsewhere that at large enough electron-phonon coupling the ground state of this model with a large applied magnetic field is a mixed bipolaronic-polaronic configuration (at any band filling and at any dimension). In the half-filled case we propose as ground state for these polarons and bipolarons an ordered structure, which turns out to be equivalent to a periodic (or quasi-periodic) array of neutral solitons and which appears physically as spin density waves. We describe new improved numerical techniques for calculating these configurations and their energy. The magnetization as a function of the magnetic field is found to vary as a devil's staircase, each plateau corresponding to a commensurate array of neutral solitons. The first plateau corresponds to a structure with no neutral soliton, while the magnetic threshold field required to cross its edge corresponds to the energy of this neutral soliton. In analogy with the Frenkel-Kontorowa (FK) model this devil's staircase is believed to be incomplete if there is an analytic incommensurate array of neutral solitons (k<1.8), and complete otherwise. The magnetic threshold field required to observe the beginning of these devil's staircases could be accessible in real charge density waves, if their electronic gap (which is found to be about four times the energy of the neutral soliton) does not range beyond 100 K.

Generation of a periodic array of dark spatial solitons in the regime of effective amplification

We experimentally demonstrate the generation of a periodic array of dark spatial solitons from two plane waves propagating at some angle in the regime of adiabatic amplification in a Kerr-like medium. The importance of amplification for the generation of clean dark solitons is shown. The combined action of nonlinearity, diffraction, and amplification leads to the reshaping of the input signal into an array of dark solitons with flat phase fronts in the bright background region.

Modulation of the output of an XeCl* laser by the generation of electrical solitons

A new technique is reported for exciting an XeCl* excimer laser to produce a sequence of high recurrence frequency output pulses. An electrical soliton array is generated within the pulsed power driving circuit using a discrete-component transmission line containing nonlinear ferroelectric capacitors. The method offers several advantages over alternative electrooptical means of laser output modulation.

All-optical steering of dark spatial soliton arrays and the beams guided by them

We experimentally demonstrate all-optical steering of arrays of dark spatial solitons. The arrays are generated by two intersecting plane waves in the regime of adiabatic amplification in a Kerr-like medium. The steering is achieved by changing the relative intensities of the beams. In addition, we show that beams guided in the soliton channels can also be scanned.

Methods of theoretical analysis and computer modeling of the shaping of electrical pulses by nonlinear transmission lines and lumped-element delay lines

The mechanism by which high-power electrical pulses can be sharpened by propagation along nonlinear transmission lines and lumped-element delay lines is described with emphasis on the production of pulses with very fast leading or trailing edges. A survey of some of the mathematical techniques that have been applied to the propagation of electrical signals along nonlinear lines and ladder networks is presented, and the limitations of these techniques are discussed. The processes that both produce and limit pulse sharpening on nonlinear lumped-element delay lines are examined, and it is found that the wave equation, which describes the propagation of electrical signals along such networks, predicts that an electrical pulse will decompose into an array of solitons. An approximate formula for estimating the degree of pulse sharpening that can be produced on a delay line with a given number of sections is derived, and its accuracy is compared with experimental results. Numerical integration techniques for solving the nonlinear differential and difference equations that result from the mathematical analysis of nonlinear lines and networks are discussed, and the propagation of a voltage pulse along a lumped-element delay line containing nonlinear capacitors is simulated using a computer model based on an efficient algorithm.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>