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At least 145 records · Page 8Linked to original sources
arXiv1999

The moment method in general Nonlinear Schrodinger Equations

In this paper we develop a new approximation method valid for a wide family of nonlinear wave equations of Nonlinear Schrödinger type. The result is a reduced set of ordinary differential equations for a finite set of parameters measuring global properties of the solutions, named momenta. We prove that these equations provide exact results in some relevant cases and show how to impose reasonable approximations that can be regarded as a perturbative approach and as an extension of the time dependent variational method.

patt-sol↗
arXiv1999

Stability of multi-parameter solitons: Asymptotic approach

General asymptotic approach to the stability problem of multi-parameter solitons in Hamiltonian systems $i\partial E_n/\partial z=δH/δE_n^*$ has been developed. It has been shown that asymptotic study of the soliton stability can be reduced to the calculation of a certain sequence of the determinants, where the famous determinant of the matrix consisting from the derivatives of the system invariants with respect to the soliton parameters is just the first in the series. The presented approach gives first analytical criterion for the oscillatory instability and also predicts novel stationary instability. Higher order approximations allow to calculate corresponding eigenvalues with arbitrary accuracy.

patt-sol↗
arXiv1999

Instabilities of Higher-Order Parametric Solitons. Filamentation versus Coalescence

We investigate stability and dynamics of higher-order solitary waves in quadratic media, which have a central peak and one or more surrounding rings. We show existence of two qualitatively different behaviours. For positive phase mismatch the rings break up into filaments which move radially to initial ring. For sufficient negative mismatches rings are found to coalesce with central peak, forming a single oscillating filament.

patt-sol↗
arXiv1999

Dispersion relations to oscillatory reaction-diffusion systems with the self-consistent flow

Dispersion curves to a oscillatory reaction-diffusion system with the self-consistent flow have obtained by means of numerical calculations. The flow modulates the shape of dispersion curves and characteristics of traveling waves. The point of inflection which separates the dispersion curves into two branches corresponding to trigger and phase waves, moves according to the value of the advection constant. The dynamics of phase wave in reaction-diffusion-advection equations has been studied by limit cycle perturbations. The dispersion relation obtained from the phase equation shows that the competition between diffusion and advection constants modulates the oscillation frequency from the bulk oscillation in the long-wave dynamics. Such a competition implies that phase waves with the flow have a wider variety of dynamics than waves without the flow.

patt-sol↗
arXiv1999

Modelling the dynamics of turbulent floods

Consider the dynamics of turbulent flow in rivers, estuaries and floods. Based on the widely used k-epsilon model for turbulence, we use the techniques of centre manifold theory to derive dynamical models for the evolution of the water depth and of vertically averaged flow velocity and turbulent parameters. This new model for the shallow water dynamics of turbulent flow: resolves the vertical structure of the flow and the turbulence; includes interaction between turbulence and long waves; and gives a rational alternative to classical models for turbulent environmental flows.

patt-sol↗
arXiv1999

Electric Nusselt number characterization of electroconvection in nematic liquid crystals

We develop a characterization method of electroconvection structures in a planar nematic liquid crystal layer by a study of the electric current transport. Because the applied potential difference has a sinusoidal time dependence, we define two electric Nusselt numbers corresponding to the in-phase and out-of-phase components of the current. These Nusselt numbers are predicted theoretically using a weakly nonlinear analysis of the standard model. Our measurements of the electric current confirm that both numbers vary linearly with the distance from onset until the occurence of secondary instabilities; these instabilities also have a distinct Nusselt number signature. A systematic comparison between our theoretical and experimental results, using no adjusted parameters, demonstrates reasonable agreement. This represents a quantitative test of the standard model completely independent from traditional, optical techniques of studying electroconvection.

patt-sol↗
arXiv1999

Bifurcation Phenomena in Optimal Velocity Model for Traffic Flows

In the optimal velocity model with a time lag, we show that there appear multiple exact solutions in some ranges of car density, describing a uniform flow, a stable and an unstable congested flows. This establishes the presence of subcritical Hopf bifurcations. Our analytic results have far-reaching implications for traffic flows such as hysteresis phenomena associated with discontinuous transitions between uniform and congested flows.

patt-sol↗
arXiv1999

Crystallization Kinetics in the Swift--Hohenberg Model

It is shown numerically and analytically that the front propagation process in the framework of the Swift-Hohenberg model is determined by periodic nucleation events triggered by the explosive growth of the localized zero-eigenvalue mode of the corresponding linear problem. We derive the evolution equation for this mode using asymptotic analysis, and evaluate the time interval between nucleation events, and hence the front speed. In the presence of noise, we derive the velocity exponent of ``thermally activated'' front propagation (creep) beyond the pinning threshold.

patt-sol↗
arXiv1999

Longwave Interface Instability In Two-Fluid Vibrational Flow

We consider longwave mode of the interface instability in the system comprising of two immiscible fluid layers. The fluids fill out plane horizontal cavity which is subjected to horizontal harmonic vibration. The analysis is performed within the framework of "high frequency of the vibration" approximation and the averaging procedure. The nonlinear equation (having the form of Newton's second law) for the amplitude of interface deformation is obtained by means of multiple scales method. It is shown that (in addition to previously detected quasistationary periodic solutions) the equation has a class of quasistationary solitary solutions.

patt-sol↗
arXiv2000

A Particle Model of Rolling Grain Ripples Under Waves

A simple model is presented for the formation of rolling grain ripples on a flat sand bed by the oscillatory flow generated by a surface wave. An equation of motion is derived for the individual ripples, seen as "particles", on the otherwise flat bed. The model account for the initial apperance of the ripples, the subsequent coarsening of the ripples and the final equilibrium state. The model is related to physical parameters of the problem, and an analytical approximation for the equilibrium spacing of the ripples is developed. It is found that the spacing between the ripples scale with the square-root of the non-dimensional shear stress (the Shields parameter) on a flat bed. The results of the model are compared with measurements, and reasonable agreement between the model and the measurements is demonstrated.

patt-sol↗
arXiv1999

Instanton solutions in the problem of wrinkled flame front dynamics

The statistics of wrinkling flame front is invetigated by the quantum filed theory methods. We dwell on the WKB approximation in the functional integral which is analogous to the Wyld functional integral in turbulence. The main contribution to statistics is due to a coupled field-force configuration. This configuration is related to a kink between metastable exact pole solutions of the Syvashinsky equation. These kinks are responsible for both the formation of new cusps and the rapid power-law acceleration of the mean flame-front. The problem of asymptotic stability of the solutions is discussed.

patt-sol↗
arXiv1999

1/f noise in spatially extended systems with order-disorder phase transitions

Noise power spectra in spatially extended dynamical systems are investigated, using as a model the Complex Ginzburg-Landau equation with a stochastic term. Analytical and numerical investigations show that the temporal noise spectra are of 1/f^a form, where a=2-D/2 with D the spatial dimension of the system. This suggests that nonequilibrium order-disorder phase transitions may play a role for the universally observed 1/f noise.

patt-sol↗
arXiv2000

Pulse Shepherding and Multi-Channel Soliton Transmission in Bit-Parallel-Wavelength Optical Fiber Links

We study bit-parallel-wavelength (BPW) pulse transmission in multi-channel single-mode optical fiber links for high-performance computer networks. We develop a theory of the pulse shepherding effect earlier discovered in numerical simulations, and also describe the families of the BPW solitons and bifurcation cascades in a system of N coupled nonlinear Schrödinger equations.

patt-sol↗
arXiv1997

Parallel Implementations of the Split-Step Fourier Method for Solving Nonlinear Schrödinger Systems

We present a parallel version of the well-known Split-Step Fourier method (SSF) for solving the Nonlinear Schrödinger equation, a mathematical model describing wave packet propagation in fiber optic lines. The algorithm is implemented under both distributed and shared memory programming paradigms on the Silicon Graphics/Cray Research Origin 200. The 1D Fast-Fourier Transform (FFT) is parallelized by writing the 1D FFT as a 2D matrix and performing independent 1D sequential FFTs on the rows and columns of this matrix. We can attain almost perfect speedup in SSF for small numbers of processors depending on both problem size and communication contention. The parallel algorithm is applicable to other computational problems constrained by the speed of the 1D FFT.

physics.comp-ph↗
arXiv1998

Asymptotic Theory of Particle Trapping in Coherent Nonlinear Alfven Waves

A fully nonlinear, time-asymptotic theory of resonant particle trapping in large-amplitude quasi-parallel Alfven waves is presented. The effect of trapped particles on the nonlinear dynamics of quasi-stationary Alfvenic discontinuities and coherent Alfven waves is highly non-trivial and forces to a significant departure of the theory from the conventional DNLS and KNLS equation models. The virial theorem is used to determine the time-asymptotic distribution function.

physics.plasm-ph↗
arXiv1998

Solitary Waves on a Coasting High-Energy Stored Beam

In this work we derive evolution equations for the nonlinear behavior of a coasting beam under the influence of a resonator impedance. Using a renormalization group approach we find a set of coupled nonlinear equations for the beam density and the resonator voltage. Under certain conditions, these may be analytically solved yielding solitary wave behavior, even in the presence of significant dissipation in the resonator. We find long-lived perturbations, i.e. droplets, which separate from the beam and decelerate towards a quasi-equilibrium state, in good agreement with simulation results.

physics.acc-ph↗
arXiv1998

Coherent Nonlinear Phenomena in High Energy Synchrotrons: Observations and Theoretical Models

Nonlinear waves have been observed in synchrotrons for years but have received little attention in the literature. While pathological, these phenomena are worth studying on at least two accounts. First, the formation of solitary waves may lead to droplet formation that causes significant beam halo to develop. Secondly, a variety of nonlinear processes are likely involved in the normal saturation of unstable oscillations, leading to the possibility that low-level, but potentially broadband fluctuation spectra may develop. Both features carry indirectly the signature of the machine impedance. In this work we review a number of observations of nonlinear longitudinal waves made in Fermilab accelerators, and make a first attempt to develop appropriate theoretical models to explain these observations.

physics.acc-ph↗