Discrete solitons and vortices in hexagonal and honeycomb lattices: Existence, stability, and dynamics

We consider a prototypical dynamical lattice model, namely, the discrete nonlinear Schrodinger equation on nonsquare lattice geometries. We present a systematic classification of the solutions that arise in principal six-lattice-site and three-lattice-site contours in the form of both discrete multipole solitons and discrete vortices. Additionally to identifying the possible states, we analytically track their linear stability both qualitatively and quantitatively. We find that among the six-site configurations, the

Higher-order effects and ultrashort solitons in left-handed metamaterials

Starting from Maxwell's equations, we use the reductive perturbation method to derive a second-order and a third-order nonlinear Schrodinger equation, describing ultrashort solitons in nonlinear left-handed metamaterials. We find necessary conditions and derive exact bright and dark soliton solutions of these equations for the electric and magnetic field envelopes.

Electromagnetic envelope solitons in magnetized plasma

A multiple scales technique is employed to solve the fluid-Maxwell equations describing a weakly nonlinear circularly polarized electromagnetic pulse in magnetized plasma. A nonlinear Schrodinger-type (NLS) equation is shown to govern the amplitude of the vector potential. The conditions for modulational instability and for the existence of various types of localized envelope modes are investigated in terms of relevant parameters. Right-hand circularly polarized (RCP) waves are shown to be modulationally unstable regardless of the value of the ambient magnetic field and propagate as bright-type solitons. The same is true for left-hand circularly polarized (LCP) waves in a weakly to moderately magnetized plasma. In other parameter regions, LCP waves are stable in strongly magnetized plasmas and may propagate as dark-type solitons (electric field holes). The evolution of envelope solitons is analyzed numerically, and it is shown that solitons propagate in magnetized plasma without any essential change in amplitude and shape. (C) 2009 Elsevier B.V. All rights reserved.

Nonlinear modulation of ion-acoustic waves in two-electron-temperature plasmas

The amplitude modulation of ion-acoustic waves IS investigated in a plasma consisting of adiabatic warm ions, and two different populations of thermal electrons at different temperatures. The fluid equations are reduced to nonlinear Schrodinger equation by employing a multi-scale perturbation technique. A linear stability analysis for the wave packet amplitude reveals that long wavelengths are always stable, while modulational instability sets in for shorter wavelengths. It is shown that increasing the value of the hot-to-cold electron temperature ratio (mu), for a given value of the hot-to-cold electron density ratio (nu): favors instability. The role of the ion temperature is also discussed. In the limiting case nu = 0 (or nu -> infinity). which correspond(s) to an ordinary (single) electron-ion plasma, the results of previous works are recovered.

Relativistic laser pulse compression in plasmas with a linear axial density gradient

The self-compression of a relativistic Gaussian laser pulse propagating in a non-uniform plasma is investigated. A linear density inhomogeneity (density ramp) is assumed in the axial direction. The nonlinear Schrodinger equation is first solved within a one-dimensional geometry by using the paraxial formalism to demonstrate the occurrence of longitudinal pulse compression and the associated increase in intensity. Both longitudinal and transverse self-compression in plasma is examined for a finite extent Gaussian laser pulse. A pair of appropriate trial functions, for the beam width parameter (in space) and the pulse width parameter (in time) are defined and the corresponding equations of space and time evolution are derived. A numerical investigation shows that inhomogeneity in the plasma can further boost the compression mechanism and localize the pulse intensity, in comparison with a homogeneous plasma. A 100 fs pulse is compressed in an inhomogeneous plasma medium by more than ten times. Our findings indicate the possibility for the generation of particularly intense and short pulses, with relevance to the future development of tabletop high-power ultrashort laser pulse based particle acceleration devices and associated high harmonic generation. An extension of the model is proposed to investigate relativistic laser pulse compression in magnetized plasmas.

Fokker-Planck equation for a test-particle weakly coupled to a magnetized plasma

We consider the derivation of a kinetic equation for a charged test particle weakly interacting with an electrostatic plasma in thermal equilibrium, subject to a uniform external magnetic field. The Liouville equation leads to a generalized master equation to second order in the `weak' interaction; a Fokker-Planck-type equation then follows as a `Markovian' approximation. It is shown that such an equation does not preserve the positivity of the distribution function f(x,v;t). By applying techniques developed in the theory of open systems, a correct Fokker-Planck equation is derived. Explicit expressions for the diffusion and drift coefficients, depending on the magnetic field, are obtained.

A comparison of nonstaggered compact FDTD schemes for the 3D wave equation

This paper aims at providing a better insight into the 3D approximations of the wave equation using compact finite-difference time-domain (FDTD) schemes in the context of room acoustic simulations. A general family of 3D compact explicit and implicit schemes based on a nonstaggered rectilinear grid is analyzed in terms of stability, numerical error, and accuracy. Various special cases are compared and the most accurate explicit and implicit schemes are identified. Further considerations presented in the paper include the direct relationship with other numerical approaches found in the literature on room acoustic modeling such as the 3D digital waveguide mesh and Yee's staggered grid technique.

Berry phase in open quantum systems: a quantum Langevin equation approach

The evolution of a two level system with a slowly varying Hamiltonian, modeled as a spin 1/2 in a slowly varying magnetic field, and interacting with a quantum environment, modeled as a bath of harmonic oscillators is analyzed using a quantum Langevin approach. This allows to easily obtain the dissipation time and the correction to the Berry phase in the case of an adiabatic cyclic evolution.

Electrostatic solitary waves in the presence of excess superthermal electrons: modulational instability and envelope soliton modes

The nonlinear dynamics of electrostatic solitary waves in the form of localized modulated wavepackets is investigated from first principles. Electron-acoustic (EA) excitations are considered in a two-electron plasma, via a fluid formulation. The plasma, assumed to be collisionless and uniform (unmagnetized), is composed of two types of electrons (inertial cold electrons and inertialess kappa-distributed superthermal electrons) and stationary ions. By making use of a multiscale perturbation technique, a nonlinear Schrodinger equation is derived for the modulated envelope, relying on which the occurrence of modulational instability (MI) is investigated in detail. Stationary profile localized EA excitations may exist, in the form of bright solitons (envelope pulses) or dark envelopes (voids). The presence of superthermal electrons modifies the conditions for MI to occur, as well as the associated threshold and growth rate. The concentration of superthermal electrons (i.e., the deviation from a Maxwellian electron distribution) may control or even suppress MI. Furthermore, superthermality affects the characteristics of solitary envelope structures, both qualitatively (supporting one or the other type, for different.) and quantitatively, changing their characteristics (width, amplitude). The stability of bright and dark-type nonlinear structures is confirmed by numerical simulations.

CRITICAL PROCESSES, LANGEVIN EQUATION AND UNIVERSALITY

In nature there are ubiquitous systems that can naturally approach critical states, The Langevin equation in the discrete version can be used to describe a class of critical processes, which are characterized by power-law behaviors and scaling relations. As an example, we present a simple model for a clinical thermometer, whose reading cannot fall even when its temperature decreases. The fibers bundle model and the spring-block model are also shown to belong to such a class.

Collapse versus growth for a Bose-Einstein condensate with attractive interactions

Using a model potential approach, we study the time-dependent behavior of a Bose-Einstein condensate with negative scattering length during its collapse in the zero-temperature limit. The condensate is modeled through an effective potential, which linearizes the Schrodinger equation, in order to obtain an intuitive visualization of the dynamics of the condensate. We find that a substantial fraction of the condensate survives the collapse. The origin for this survival is the reappearance of a barrier in the effective potential during the collapse. In contrast to previous calculations, the present calculations indicate that the size of the residual condensate strongly depends on the growth rate of the condensate. The present results are compared to other theoretical calculations and to experimental work.

Note on the single-shock solutions of the Korteweg-de Vries-Burgers equation

The well-known shock solutions of the Korteweg-de Vries-Burgers equation are revisited, together with their limitations in the context of plasma (astro)physical applications. Although available in the literature for a long time, it seems to have been forgotten in recent papers that such shocks are monotonic and unique, for a given plasma configuration, and cannot show oscillatory or bell-shaped features. This uniqueness is contrasted to solitary wave solutions of the two parent equations (Korteweg-de Vries and Burgers), which form a family of curves parameterized by the excess velocity over the linear phase speed.

Nonlinear wavepackets in pair-ion and electron-positron-ion plasmas

The occurrence of amplitude-modulated electrostatic and electromagnetic
wavepackets in pair plasmas is investigated. A static additional charged background species is considered, accounting for dust defects or for heavy ion
presence in the background. Relying on a two-fluid description, a nonlinear
Schrodinger type evolution equation is obtained and analyzed, in terms of the
slow dynamics of the wave amplitude. Exact envelope excitations are obtained,
modelling envelope pulses or holes, and their characteristics are discussed.