We study the two-soliton interaction dynamics within the framework of a fully integrable model, i.e., the Gardner equation with negative cubic nonlinearity, which admits the existence of a limiting soliton. The features of the soliton interaction with participation of a thick soliton are demonstrated. Special attention is paid to the nonlinear-interaction influence on the moments of the wave fields, which determine the skewness and the kurtosis in the theory of turbulence.
Equations for the wave perturbations of velocity and pressure in a nonisothermal atmosphere are considered. It is noted that the pressure perturbation has singularities near the altitude where the equality of the horizontal phase velocity of the perturbation and sound velocity in the medium is fulfilled. At this altitude, a thin atmospheric layer with finite mass is concentrated. The wave perturbations do not penetrate to a higher level. The presence of a singularity in the wave perturbation of pressure was numerically confirmed for the actual altitude temperature profiles of the atmosphere.
We show that the discrete frequency spectrum of a plane hydrodynamic flow of ideal incompressible liquid with localized trajectories of the liquid particles can contain only one, two, or an infinite number of harmonics.
We report on the latest achievements in the development of superconducting hot-electron bolometer (HEB) mixers for terahertz superheterodyne receivers. We consider application ranges of such receivers and requirements for the basic characteristics of the mixers. Main features of the mixers, such as noise temperature, gain bandwidth, noise bandwidth, and required local-oscillator power, have been improved significantly over the past few years due to intense research work, both in terms of the element fabrication quality and in terms of understanding of the physics of the processes occurring in the HEB mixers. Contacts between the superconducting bridge and the planar antenna play a key role in the mixer operation. Improvement of the quality of the contacts leads simultaneously to a decrease in the noise temperature and an increase in the gain bandwidth of a mixer.
We study interaction of different-polarization single-component vector solitons of the envelope function in anisotropic media within the framework of the system of two coupled third-order nonlinear SchrЁodinger equations which allow for the third-order linear dispersion, nonlinear dispersion, nonlinear cross-phase modulation, and cross-nonlinear dispersion. The regimes of mutual reflection, passage, and asymptotic approach of the solitons are obtained. It is shown that the character of interaction of such solitons is determined by the initial relationship of their amplitudes and phases. The stationary mutual locations of interacting solitons and their coupled, the so-called breather states are discussed. The roles of the cubic nonlinearity, cubic cross-nonlinearity, and cross-nonlinear dispersion during interaction of solitons are studied.
The stationary waves with nonlinear phase modulation in an extended nonlinear Schrödinger equation with nonlinear dispersion and stimulated Raman–scattering terms are considered. New class of a kink–waves are found. This waves exists as the result of balance of the stimulated Raman–scattering and nonlinear dispersion
We study stability of a synchronous regime in hub clusters of the power networks, which are simulated by ensembles of phase oscillators. An approach allowing one to estimate the regions in the parameter space, which correspond to the global asymptotic stability of this regime, is presented. The method is illustrated by an example of a hub cluster consisting of one generator and two consumers.
In part I of this work , we study the dispersion characteristics of low-frequency waves in a relativistic electron–positron plasma. In part II, we examine the electromagnetic wave instability in this plasma caused by an admixture of nonrelativistic protons with energy comparable with the energy of relativistic low-mass particles. The instability occurs in the frequency band between the fundamental harmonic of proton gyrofrequency and the fundamental harmonic of relativistic electron gyrofrequency. The results can be used for the interpretation of known observations of the pulsar emissions obtained with a high time and frequency resolution. The considered instability can probably be the initial stage of the microwave radio emission nanoshots typical of the pulsar in the Crab Nebula. © 2016, Springer Science+Business Media New York.
We consider the dispersion characteristics of electromagnetic waves in a plasma with strong magnetic field and equal content of relativistic electrons and positrons, whose synchrotron radiation can be the source of optical radiation of a pulsar. It is shown that when a small fraction of nonrelativistic protons with a nonequilibrium distribution function is present in the plasma, an effective instability can develop at frequencies below the first harmonic of the relativistic gyrofrequency of electrons, namely, at the harmonics of the proton gyrofrequency. This instability leads to the excitation of the O- and X-mode electromagnetic waves, which can, in principle, be related with the observed pulsar radiation. In part I of this paper, we study dispersion characteristics of low-frequency electromagnetic waves (with frequencies below the relativistic gyrofrequency of electrons) in an ultrarelativistic electron-positron plasma with an isotropic momentum distribution function of the particles. Instabilities of the O- and X-mode waves and the conditions of escape of the radiation from the region of strong magnetic field into a rarefied isotropic plasma will be considered in paper II. The results can be used in the interpretation of known experimental data on the dynamic pulsar radiation spectra obtained with high temporal and frequency resolution.
We present the results of experimental studies of the basic characteristics and operation features of a terahertz heterodyne detector based on the superconducting NbN HEB mixer and a quantum cascade laser as a local oscillator operating at a frequency of 2.02 THz. The measured noise temperature of such a mixer amounted to 1500 K. The spectral resolution of the detector is determined by the width of the local-oscillator spectral line whose measured value does not exceed 1 MHz. The quantum-cascade laser could be linearly tuned with respect to frequency with the coefficient 7.2 MHz/mA within the limits of the current oscillation bandwidth.
Evolution of solitons is addressed in the framework of an extended nonlinear Schrödinger equation (NLSE), including a pseudo-stimulated-Raman-scattering (pseudo-SRS) term, i.e., a spatial-domain counterpart of the SRS term which is well known as an ingredient of the temporal-domain NLSE in optics. In the present context, it is induced by the underlying interaction of the high-frequency envelope wave with a damped low-frequency wave mode. Also included is spatial inhomogeneity of self-phase modulation (SPM). It is shown that the wavenumber downshift of solitons, caused by the pseudo-SRS, may be compensated by an upshift provided by the increasing SPM coefficient. An analytical solution for solitons is obtained in an approximate form. Analytical and numerical results agree well
We consider the soliton dynamics in terms of the extended nonlinear Schr¨odinger equation taking into account the inhomogeneous linear second-order dispersion (SOD) and stimulated scattering by damped low-frequency waves (SSDW). It is shown that the wave number downshift due to SSDW is compensated by an upshift due to the SOD decrease on the spatial coordinate. A new class of stationary nonlinear localized solutions (solitons) arising as an equilibrium of SSDW and decreasing spatial SOD is found analytically within the framework of the extended inhomogeneous nonlinear Schr¨odinger equation. A regime of the dynamic equilibrium of SSDW and inhomogeneous dispersive medium with the soliton parameters periodically varied in time is found. Analytical and numerical results are in good agreement for this regime.
We propose a method for the analysis of groups of unidirectional waves on the surface of deep water, which is based on spectral data of the scattering problem in the approximation of a nonlinear Schrodinger equation. The main attention is paid to the robustness and accuracy of the numerically obtained spectral data. Various methods of choosing the wave number of the carrier wave, which rely on the analysis of the local Fourier transform and the zero-crossing wave analysis, are considered. The most robust wave numbers have been chosen on the basis of two model examples. A method for improving the accuracy of the soliton amplitude prediction, which uses the “feedback” in solving the associated scattering problem, is proposed. In the wave steepness range from 0.15 to 0.30, the accuracy of determining the amplitude of the soliton group by this technique lies in a range of 10%.
The existence of traveling waves in a strongly inhomogeneous magnetized plasma is studied. It is shown that under certain conditions for characteristics of the medium, the waves do not reflect from inhomogeneities, although their amplitude and phase vary in space. Such reflectionless waves are found mathematically as solutions of wave equations with constant coefficients, to which the original equations with variable coefficients are reduced after a certain transformation. The existence of reflectionless waves in various plasma configurations is established.
Interaction of single-component different-polarization vector solitons of the enveloping function in anisotropic media is studied within the framework of the system of two coupled third-order nonlinear Schrödinger equations which allow for the third-order linear dispersion, nonlinear dispersion, crossed nonlinear phase modulation, and crossed nonlinear dispersion. The regimes of mutual reflection, passing, and asymptotic approaching of the solitons are obtained. It is shown that the character of interaction of such solitons is determined by the initial relationship among both their amplitudes and phases. The stationary mutual locations of interacting solitons and their coupled, the so-called breather states are discussed. The roles of the cubic nonlinearity, crossed cubic nonlinearity, and crossed nonlinear dispersion during interaction of solitons are studied.
Properties of the waves, which can propagate in magnetized plasma in the frequency range below the proton gyrofrequency, depend strongly on the ion composition of the plasma. Addition of a new sort of ions leads to appearance of a new resonance frequency, at which the refractive index becomes infinite, and a new cutoff frequency, at which the refractive index becomes zero. In this case, the topology of frequency dependence of the squared refractive index changes. Specifically, a new oscillation branch appears, which is located above the cutoff frequency. A question arises whether these oscillations are excited, if radiation with the corresponding frequency, which propagates in a different mode, is present in the plasma. A linear transformation of the waves is another important effect, which is related to variations in the ion plasma composition. These two issues, which are directly related to the theory of formation of proton whistlers in the ionospheres, where the ion composition varies with altitude, are considered in this work.
The stationary waves with nonlinear phase modulation in an extended nonlinear Schrödinger equation with nonlinear dispersion and stimulated Raman–scattering terms are considered. New class of a kink–waves are found. This waves exists as the result of balance of the stimulated Raman–scattering and nonlinear dispersion.