Finite amplitude envelope solitons in pair-ion plasmas

The nonlinear coupling between finite amplitude ion thermal waves (ITWs) and quasistationary density perturbations in a pair-ion plasma is considered. A generalized nonlinear Schrödinger equation is derived for the ITW electric field envelope, accounting for large amplitude quasistationary plasma slow motion describing the ITW ponderomotive force. The present theory accounts for the trapping of ITWs in a large amplitude ion density hole. The small amplitude limit is considered and exact analytical solutions are obtained. Finite amplitude solutions are obtained numerically and their characteristics are discussed.

Nonlinear dynamics and solitons in Debye bi-crystals

The nonlinear dynamics of longitudinal dust lattice waves propagating in a dusty plasma bi-crystal is investigated. A “diatomic”-like one-dimensional dust lattice configuration is considered, consisting of two distinct dust grain species with different charges and masses. Two different frequency dispersion modes are obtained in the linear limit, namely, an optical and an acoustic wave dispersion branch. Nonlinear solitary wave solutions are shown to exist in both branches, by considering the continuum limit for lattice excitations in different nonlinear potential regimes. For this purpose, a generalized Boussinesq and an extended Korteweg de Vries equation is derived, for the acoustic mode excitations, and their exact soliton solutions are provided and compared. For the optic mode, a nonlinear Schrödinger-type equation is obtained, which is shown to possess bright- (dark-) type envelope soliton solutions in the long (short, respectively) wavelength range. Optic-type longitudinal wavepackets are shown to be generally unstable in the continuum limit, though this is shown not to be the rule in the general (discrete) case.

Electron-acoustic plasma waves: Oblique modulation and envelope solitons

Theoretical and numerical studies are presented of the amplitude modulation of electron-acoustic waves (EAWs) propagating in space plasmas whose constituents are inertial cold electrons, Boltzmann distributed hot electrons, and stationary ions. Perturbations oblique to the carrier EAW propagation direction have been considered. The stability analysis, based on a nonlinear Schrodinger equation, reveals that the EAW may become unstable; the stability criteria depend on the angle theta between the modulation and propagation directions. Different types of localized EA excitations are shown to exist.

Envelope solitons associated with electromagnetic waves in a magnetized pair plasma

The amplitude modulation of magnetic field-aligned circularly polarized electromagnetic (CPEM) waves in a magnetized pair plasma is reexamined. The nonlinear frequency shifts include the effects of the radiation pressure driven density and compressional magnetic field perturbations as well as relativistic particle mass variations. The dynamics of the modulated CPEM wave packets is governed by a nonlinear Schrodinger equation, which has attractive and repulsive interaction potentials for fast and slow CPEM waves. The modulational stability of a constant amplitude CPEM wave is studied by deriving a nonlinear dispersion from the cubic Schrodinger equation. The fast (slow) CPEM mode is modulationally unstable (stable). Possible stationary amplitude solutions of the modulated fast (slow) CPEM mode can be represented in the form of bright and dark/gray envelope electromagnetic soliton structures. Localized envelope excitations can be associated with the microstructures in pulsar magnetospheres and in laboratory pair magnetoplasmas. (C) 2005 American Institute of Physics.

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.

Dust ion acoustic solitons in a plasma with kappa-distributed electrons

Dust ion acoustic solitons in an unmagnetized dusty plasma comprising cold dust particles, adiabatic fluid ions, and electrons satisfying a kappa distribution are investigated using both small amplitude and arbitrary amplitude techniques. Their existence domain is discussed in the parameter space of Mach number M and electron density fraction f over a wide range of values of kappa. For all kappa > 3/2, including the Maxwellian distribution, negative dust supports solitons of both polarities over a range in f. In that region of parameter space solitary structures of finite amplitude can be obtained even at the lowest Mach number, the acoustic speed, for all kappa. These cannot be found from small amplitude theories. This surprising behavior is investigated, and it is shown that f(c), the value of f at which the KdV coefficient A vanishes, plays a critical role. In the presence of positive dust, only positive potential solitons are found. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3400229]

Nonlinear excitations in strongly-coupled plasma lattices: envelope solitons, kinks and intrinsic localized modes

Ensembles of charged particles (plasmas) are a highly complex form of matter, most often modeled as a many-body system characterized by weak inter-particle interactions (electrostatic coupling). However, strongly-coupled plasma configurations have recently been produced in laboratory, either by creating ultra-cold plasmas confined in a trap or by manipulating dusty plasmas in discharge experiments. In this paper, the nonlinear aspects involved in the motion of charged dust grains in a one-dimensional plasma monolayer (crystal) are discussed. Different types of collective excitations are reviewed, and characteristics and conditions for their occurrence in dusty plasma crystals are discussed, in a quasi-continuum approximation. Dust crystals are shown to support nonlinear kink-shaped supersonic solitary longitudinal excitations, as well as modulated envelope localized modes associated with longitudinal and transverse vibrations. Furthermore, the possibility for intrinsic localized modes (ILMs) — Discrete Breathers (DBs) — to occur is investigated, from first principles. The effect of mode-coupling is also briefly considered. The relation to previous results on atomic chains, and also to experimental results on strongly-coupled dust layers in gas discharge plasmas, is briefly discussed.

Large acoustic solitons and double layers in plasmas with two positive ion species

Large nonlinear acoustic waves are discussed in a plasma made up of cold supersonic and adiabatic subsonic positive ions, in the presence of hot isothermal electrons, with the help of Sagdeev pseudopotential theory. In this model, no solitons are found at the acoustic speed, and no compositional parameter ranges exist where solutions of opposite polarities can coexist. All nonlinear modes are thus super-acoustic, but polarity changes are possible. The upper limits on admissible structure velocities come from different physical arguments, in a strict order when the fractional cool ion density is increased: infinite cold ion compression, warm ion sonic point, positive double layers, negative double layers, and finally, positive double layers again. However, not all ranges exist for all mass and temperature ratios. Whereas the cold and warm ion sonic point limitations are always present over a wide range of mass and temperature ratios, and thus positive polarity solutions can easily be obtained, double layers have a more restricted existence range, specially if polarity changes are sought. (C) 2011 American Institute of Physics. [doi:10.1063/1.3579397]