Low-frequency relativistic electromagnetic solitons in collisionless plasmas

A relativistic electromagnetic soliton solution in the model of a one-dimensional, unbounded, cold, collisionless plasma is obtained without using the envelope approximation. The breaking of solitons with over-critical amplitudes is observed. The stability of undercritical solitons and the breaking of overcritical solitons are demonstrated by a particle-in-cell computer simulation. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 1, 33–38 (10 July 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Formation and dynamics of relativistic electromagnetic solitons in plasmas containing high-and low-energy electron components

We present theoretical and numerical studies of the nonlinear interactions between intense electromagnetic waves in plasmas containing high-and low-energy electron components. Such plasmas are frequently observed in laser-plasma experiments, where the hot electron component is created by the acceleration of electrons by strong electrostatic waves that are created by the laser-induced Raman forward and backward instabilities. The two-component electron plasma is described by the Vlasov equation for the hot electrons and the hydrodynamic equations for the cold electrons, which are coupled nonlinearly to the electromagnetic wave equation and the Poisson equation for the potential. The present nonlinear system is shown to admit electromagnetic solitary waves correlated with a positive potential and trapped electron islands from the hot electron population. The text was submitted by the authors in English.     

Few-cycle relativistic solitons in plasmas

A set of exact one-dimensional solutions to coupled nonlinear equations describing the propagation of a relativistic ultrashort circularly polarized laser pulse in a cold collisionless and bounded plasma where electrons have an initial velocity in the laser propagating direction is presented. The solutions investigated here are in the form of quickly moving envelop solitons at a propagation velocity comparable to the light speed. The features of solitons in both underdense and overdense plasmas with electrons having different given initial velocities in the laser propagating direction are described. It is found that the amplitude of solitons is larger and soliton width shorter in plasmas where electrons have a larger initial velocity. In overdense plasmas, soliton duration is shorter, the amplitude higher than that in underdense plasmas where electrons have the same initial velocity.     

KdV-type solitons in multicomponent relativistic plasmas

A reductive perturbation technique is used to derive modified Korteweg-deVries (KdV) equations with different degrees of isothermality in a plasma, in order to study the existence and behavior of ion-acoustic solitary wave propagation ingoing in a multicomponent relativistic plasma. The solutions of the KdV equations are obtained. It is found that the presence of multiple ions and electrons in the relativistic plasma causes a different behavior regarding the formation of solitons in plasmas.     

Three-dimensional dissipative optical solitons

A brief overview of recent theoretical results in the area of three-dimensional dissipative optical solitons is given. A systematic analysis demonstrates the existence and stability of both fundamental (spinless) and spinning three-dimensional dissipative solitons in both normal and anomalous group-velocity regimes. Direct numerical simulations of the evolution of stationary solitons of the three-dimensional cubic-quintic Ginzburg-Landau equation show full agreement with the predictions based on computation of the instability eigenvalues from the linearized equations for small perturbations. It is shown that the diffusivity in the transverse plane is necessary for the stability of vortex solitons against azimuthal perturbations, while fundamental (zero-vorticity) solitons may be stable in the absence of diffusivity. It has also been found that, at values of the nonlinear gain above the upper border of the soliton existence domain, the three-dimensional dissipative solitons either develop intrinsic pulsations or start to expand in the temporal (longitudinal) direction keeping their structure in the transverse spatial plane. Presented at 9-th International Workshop on Nonlinear Optics Applications, NOA 2007, May 17–20, 2007, Świnoujście, Poland     

The formation of relativistic electromagnetic solitons in plasma Bragg gratings induced by two counter-propagating laser pulses

The generation of relativistic electromagnetic solitons in plasma with spatiotemporal density modulation is investigated. When two counter-propagating laser pulses overlap in underdense plasma, the interaction between the pulses and plasma modulates the electron and ion densities resulting in localized, stable, long-living relativistic electromagnetic solitons. They are caused by the Stimulated Raman Scattering instability. The dependence of the formation of relativistic electromagnetic solitons on the ion motion, plasma parameters, and laser parameters is studied by particle-in-cell simulations as well.     

On relativistic electromagnetic fluid flows

In this paper we have explored certain theorems of theoretical interest in the domain of finitely conducting hydromagnetic systems. These theorems elucidate the local behavior of the congruences of magnetic (electric) field lines. Furthermore, a thermally conducting electromagnetic fluid space-time with vanishing conformal divergence is also investigated.     

Polarized electromagnetic solitons in carbon nanotubes

The alternating electromagnetic field of general polarization spreading in the zigzag carbon nanotube system was studied in the case of low temperatures. The electron system of carbon nanotubes was described microscopically, omitting the interaction with the phonon system due to the extremely short pulse of the electromagnetic field. An effective equation was derived for the amplitudes of the electromagnetic field vector potential.     

Three-dimensional vortex solitons in self-defocusing media

We demonstrate that families of vortex solitons are possible in a bidispersive three-dimensional nonlinear Schr?dinger equation. These solutions can be considered as extensions of two-dimensional dark vortex solitons which, along the third dimension, remain localized due to the interplay between dispersion and nonlinearity. Such vortex solitons can be observed in optical media with normal dispersion, normal diffraction, and defocusing nonlinearity.     

Three-dimensional solitons in two-component Bose-Einstein condensates

We investigate a kind of solitons in the two-component Bose-Einstein condensates with axisymmetric configurations in the R2 × S1 space. The corresponding topological structure is referred to as Hopfion. The spin texture differs from the conventional three-dimensional （3D） skyrmion and knot, which is characterized by two homotopy invariants. The stability of the Hopfion is verified numerically by evolving the Gross-Pitaevskii equations in imaginary time.     

Truesdell invariance in relativistic electromagnetic fields

The Truesdell derivative of a contravariant tensor fieldX ^ab is defined with respect to a null congruencel ^a analogous to the Truesdell stress rate in classical continuum mechanics. The dynamical consequences of the Truesdell invariance with respect to a timelike vectoru ^a of the stress-energy tensor characterizing a charged perfect fluid with null conductivity are the conservation of pressure (p), charged density (e) an expansion-free flow, constancy of the Maxwell scalars, and vanishing spin coefficients+¯ = ¯ – = = 0 (assuming freedom conditionsk = = + ¯ = 0). The electromagnetic energy momentum tensor for the special subcases of Ruse-Synge classification for typesA andB are described in terms of the spin coefficients introduced by Newman-Penrose.     

On the envelope solitons in a relativistic ion-acoustic plasma

Summary Nonlinear Schr?dinger equation describing the envelope solitons is deduced in the case of ion-acoustic relativistic plasma, without taking recourse to the usual reductive perturbation theory. The methodology is that of Friedet al. (1973), which in some sense can be considered to be an extension of the effective (pseudo) potential theory. Amplitude and velocity of the solitary wave are obtained in terms of the physical parameters of plasma.

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Riassunto Si deriva l'equazione di Schr?dinger non lineare che descrive i solitoni dell'involucro nel caso del plasma relativistico a onde ioniche, senza fare ricorso all'usuale teoria di perturbazione riduttiva. La metodologia è quella di Friedet al. (1973) che si può considerare in qualche modo come un'estensione della teoria efficace di (pseudo) potenziale. Si ottengono l'ampiezza e la velocità dell'onda solitaria nei termini dei parametri fisici del plasma.

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Резюме Выводится нелинейное уравнение Шредингера, описывающее огибающие солитоны в случае релятивистской плазмы, без использования обычной теории возмущений. Методология аналогична методологии фрейда и др. (1973), которая в некотором смысле представляет обобщение теории эффективного (псевдо) потенциала. Получается вмплитуда и скорости одиночной волны в терминах физических параметров плазмы.

     

New class of extremely short electromagnetic solitons

A physical realization is presented for the integrable modified sine-Gordon equation. In this case, this equation describes the propagation of an extremely short vector electromagnetic pulse in the system of asymmetric quantum objects that have permanent dipole moments in the self-energy states. Using soliton solutions for ordinary and extraordinary components, new regimes of the dynamics of the pulse and medium that are specific only to asymmetric media have been found.     

Large-amplitude electromagnetic waves in relativistic plasmas

The propagation of linearly polarized large-amplitude electromagnetic waves in relativistic plasmas is studied in the framework of the Akhiezer-Polovin-model. Different forms of the basic equations are reviewed and important solutions are presented for small and critical plasma densities. The well-known periodic solutions are generalized to quasiperiodic solutions taking account of additional electrostatic oscillations.     

Three-dimensional solitons in ferrites and their stability

The study is made of soliton solution of nonlinear equations describing dynamics of some magnets as well as the field theory models. Three-dimensional solitons are analysed to which non-uniform magnetization precession corresponds.Necessary and sufficient conditions for soliton stability according to Lyapunov are obtained. The soliton without nodes is proved to be stable over a wide range of the precission frequencies and unstable beyond this range. Solitons with nodes are unstable at all frequencies.     

Relativistic electromagnetic solitons in the electron-ion plasma

We present the results of the investigation about the ion motion influence on relativistic soliton structure, and show that in the case of moving multinode solitons the effect of the ion dynamics results in the limiting of its amplitude. The constraint on the maximum amplitude corresponds to either the ion motion breaking in the low-node-number case, or to the electron trajectory self-intersection in the case of high-node-number solitons. The soliton breaking leads to the generation of fast ions, and provides a novel mechanism for the ion acceleration in the plasma irradiated by the high-intensity laser pulses.