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The problem of the seismic influence on ionosphere was being investigated by V. A. Pavlov, but the investigation did not account the nonlinear effects. In this paper, the problem is studied with a due account of weak nonlinearity and dispersion, influence of dissipation and the stochastic fluctuations of the electron density which always take a place in the ionosphere. In conclusion, the exact results for the nearest zone and for the farthest one of earthquake epicenter could be obtained in the study. The obtained results are in well accordance with the results in the complex radiophysical experiments on the network of the stations of Russia Far East region., 電離層への地震の影響の問題はV.A.Pavlov達によって調べられているが、非線形効果を考慮に入れていない。本稿では、弱い非線形性と分散、散逸効果の影響および電離層において常に生じる電子密度の確率的ゆらぎを考慮に入れてこの問題を調べた。その結果、震央に最も近い地帯と最も離れた地帯に対して正確な結果を得ることができた。得られた結果はロシア極東地域観測網での複合電波物理実験によって得られた結果と良く一致した。

The seismic activity-related oscillations of the EM (Electromagnetic) field in lower frequency than tens Hz may be observed on the Earth's surface. The EM oscillations on the Earth's surface have the electric component of the field much dominating over the magnetic component. The electric component represents the most diverse oscillations produced by atmospheric and space sources. Therefore, the identification of seismity-related emissions is hampered. Under these conditions, it is easier to identify any determinative signals of the examined electric field, if they have some established specific characters. Searching for how signals are related to their causes (the processes in the Earth's crust) is necessary. This paper outlines the activities of the new seismic data registering station in Magadan and the details of the ULF (Ultra Low Frequency)-ELF (Extremely Low Frequency) registering facilities aimed at investigating the dynamics of the ionosphere processes and the electromagnetic field within the 1 Hz-10 MHz band. Further, the combined processing of EM and seismic data distinguished into preliminary and specific processing is explained., 10Hz以下の地震性電磁波が地表面で観測される場合がある。地表面の電磁振動は電磁場の電気的成分が磁気的成分よりも支配的である。この電気的成分は大気および宇宙放射源により作られる最も多様な振動を示す。それゆえ、地震に関連した電磁放射の同定が妨げられる。これらの条件下で、もしも吟味している電場がいくつかの確定した特色を持つならば、決定的信号を同定することがより容易になる。信号がそれらの原因(地殻における諸過程)にどのように関係するるかを調べることが必要である。本稿では、マガダンにおける新しい地震データ記録ステーションの活動および電離層と1Hz-10MHzの電磁場のダイナミクスを研究することを目的としたULF(Ultra Low Frequency)-ELF(Extremely Low Frequency)記録施設の詳細を示した。予備的データ処理と特定的データ処理に区分される電磁データ/地震データ組合せ処理を説明した。

This paper presents the experimental technique and some results of the analysis of experiments on radio sounding of ionosphere in the periods of seismic activity on the Russian North East station network. The experimental system which studies the ionospheric dynamical processes associated with earthquakes, includes two subsystems: (1) a subsystem for investigating the variation of the fundamental ionospheric characteristics and the dynamics of the ionospheric plasma ionized component at height of 50 to 350 km by a ground based radio sounding; and (2) a subsystem for trans-ionospheric sounding by navigational and geostationary satellite signals. The experiment obtained some results concerning the anomalies in the ionospheric characteristics before and after earthquakes, which may be interpreted as pre and post effects of seismo-ionospheric relationships. The maximum value of the electron density anomaly in the F2 layer is capital delta-N to 10(exp 4)/cu cm. A big changing of h(sub 0)F2 layer in before shock can be also seen. The appearance and the intensification of the quasiperiodic ionospheric parameter oscillations at 1-1.5 days before and one day after the earthquake have been also observed., ロシア北東地域観測網で地震活動期間に得られた電離層のラジオ波探測サウンディングによる実験の方法および解析結果について述べた。その実験システムは地震に関連した電離層動的過程を研究するもので、2つのサブシステムを含む。(1)地上ラジオ波探測を用いて高度50-350kmで基本電離層特性の変動および電離層プラズマ電離成分のダイナミクスを研究するサブシステム、および(2)航法衛星信号と静止衛星信号により電離層横断探測するサブシステム。この実験により、おそらく地震電離層関係の事前および事後効果として解釈できる地震前後の電離層特性異常に関する諸結果を得た。F2層の電子密度異常の最大値はΔN〜10(exp 4)/立方センチメートルである。前震でh(sub 0)F2層に大きな変化も見られた。地震前1-1.5日および地震後1日で準周期的電離層パラメータ振動も観測された。

The formation, structure, stability and dynamics of multidimensional nonlinear waves and solitons in a plasma with v = -(zx(vector differential operator)psi)/B and BETA>1 are studied. To study the stability of multidimensional solitons, the variation problem of the Hamiltonian bounding with respect to deformations conserving momentum is used. To study evolution of solitons and their collision dynamics the equations are integrated numerically. It was obtained that in both cases the formation of multidimensional solitons can be observed. It is found that the soliton elastic collisions can lead to formation of complex structures including the multisoliton bound states., Pub. in International Conference on Phenomena in Ionized Gases (26th), v4 p174-175, July 2003. Prepared in cooperation with Kazan State Power Engineering University, Russia. This article is from ADA421147 International Conference on Phenomena in Ionized Gases (26th) Held in Greifswald, Germany on 15-20 July 2003. Proceedings, Volume 4

The results of numerical study of evolution and interaction of the vortex structures in the continuum, and, specifically, in plasmas and fluids in the 2D approach, when the Euler-type equations are valid, are presented. The set of the model equations e(sub i)d(sub l)x(sub i)= partial derivative(sub yi) H/B, e(sub i)d(sub l)y(sub i)= -partial derivative(sub xi) H/B, partial derivative(sub t) rho-v xDELTA rho=0, v=-(ZETAxDELTA psi)/BETA, DELTA psi = -rho describing the a continuum or quasi-particles with Coulomb interaction models, where rho is a vorticity or charge density and psi is a stream function or potential for inviscid fluid and guiding-centre plasma, respectively, and ETA is a Hamiltonian, was considered. For numerical simulation the CD method specially modified was used. in terms of vortex motion of fluids the results of numerical experiments, specifically, showed that for some conditions the interaction of vortexes in continuum may be nontrivial and, as for the "classic" FAVRs, lead to formation of complex forms of vorticity regions, for example, the vorticity filaments and sheets, and also can ended to formation of the turbulent field. The undertaken approach may be effective in studying of the atmospheric and Alfven vortex dynamics, and also useful for the interpretation of effects associated with turbulent processes in fluids and plasmas., Pub. in International Conference on Phenomena in Ionized Gases (26th), v4 p173-174, July 2003. This article is from ADA421147 International Conference on Phenomena in Ionized Gases (26th) Held in Greifswald, Germany on 15-20 July 2003. Proceedings, Volume 4

The problem of dynamics the multidimensional solitons in complex media with the dispersion is studied numerically The applications to physics of the FMS waves in a magnetized plasma, and the 2-dimensional surface waves on shallow water are discussed., Pub. in International Conference on Phenomena in Ionized Gases (26th), v4 p171, July 2003. Grant no. 01-02-16116. This article is from ADA421147 International Conference on Phenomena in Ionized Gases (26th) Held in Greifswald, Germany on 15-20 July 2003. Proceedings, Volume 4

© 2018 COSPAR The problem of stability of the multidimensional solutions of the BK class equations describing the nonlinear waves which are forming on the low-frequency branch of oscillations in plasma for cases when β≡4πnT/B2«1 and β>1 is studied. In first case, for ω<ωB=eB/Mc,kλD«1 the FMS waves are excited, and their dynamics under conditions kx2≫k⊥2, vx«cAnear the cone of θ=arctan(M/m)1/2, is described by the equation of the BK class known as the GKP equation for magnetic field h=B∼/B with due account of the high order dispersive correction defined by values of plasma parameters and angle θ=(B,k). In another case, the dynamics of the finite-amplitude Alfvén waves propagating near-to-parallel to B is described by the equation of the same class known as the 3-DNLS equation for h=(By+iBz)/2B|1-β|. To study the stability of multidimensional solutions in both cases the method of investigation of the Hamiltonian bounding with deformation conserving momentum by solving the variation problem is used. As a result, we have obtained the conditions of existence of the 2D and 3D soliton solutions in the BK system for cases of the GKP and 3-DNLS equation (i.e. for the FMS and Alfvén waves, respectively) in dependence on the equations’ coefficients, i.e. on the parameters of both plasma and wave.

© 2016, Pleiades Publishing, Ltd.On the basis of the model of the three-dimensional (3D) generalized Kadomtsev-Petviashvili equation for magnetic field h = B~/B the formation, stability, and dynamics of 3D soliton-like structures, such as the beams of fast magnetosonic (FMS) waves generated in ionospheric and magnetospheric plasma at a low-frequency branch of oscillations when β = 4πnT/B2 ≪ 1 and β > 1, are studied. The study takes into account the highest dispersion correction determined by values of the plasma parameters and the angle θ = (B, k), which plays a key role in the FMS beam propagation at those angles to the magnetic field that are close to π/2. The stability of multidimensional solutions is studied by an investigation of the Hamiltonian boundness under its deformations on the basis of solving of the corresponding variational problem. The evolution and dynamics of the 3D FMS wave beam are studied by the numerical integration of equations with the use of specially developed methods. The results can be interpreted in terms of the self-focusing phenomenon, as the formation of a stationary beam and the scattering and self-focusing of the solitary beam of FMS waves. These cases were studied with a detailed investigation of all evolutionary stages of the 3D FMS wave beams in the ionospheric and magnetospheric plasma.

© 2016, Pleiades Publishing, Ltd.On the basis of the model of the three-dimensional (3D) generalized Kadomtsev-Petviashvili equation for magnetic field h = B~/B the formation, stability, and dynamics of 3D soliton-like structures, such as the beams of fast magnetosonic (FMS) waves generated in ionospheric and magnetospheric plasma at a low-frequency branch of oscillations when β = 4πnT/B2 ≪ 1 and β > 1, are studied. The study takes into account the highest dispersion correction determined by values of the plasma parameters and the angle θ = (B, k), which plays a key role in the FMS beam propagation at those angles to the magnetic field that are close to π/2. The stability of multidimensional solutions is studied by an investigation of the Hamiltonian boundness under its deformations on the basis of solving of the corresponding variational problem. The evolution and dynamics of the 3D FMS wave beam are studied by the numerical integration of equations with the use of specially developed methods. The results can be interpreted in terms of the self-focusing phenomenon, as the formation of a stationary beam and the scattering and self-focusing of the solitary beam of FMS waves. These cases were studied with a detailed investigation of all evolutionary stages of the 3D FMS wave beams in the ionospheric and magnetospheric plasma.

© 2019, Kazan Federal University. All rights reserved. This paper considers one of the most effective methods for modeling vortical structures, which are described by the 2-dimensional equation of carry of a vortex and by the Poisson equation for a flow function, namely, the contour dynamics method based on representation of a vortical stream by finite-area vortical regions. A modification of the contour dynamics method minimizing the errors arising at its direct application to description of vortical structures has been elaborated. The examples of the results of numerical experiments on the study of the dynamics of interaction of vortical structures for various configurations of their relative positioning, signs of vorticity, and distances between borders of the finite-area vortical regions have been presented.

© 2019 IEEE. The results of numerical experiments, made on the basis of the modified CD method, on study of the dynamics of interaction of vortical structures for various configurations of their relative positioning, signs of vorticity and distances between borders of vortical regions are presented. The examples of modeling results for real vortex systems in atmosphere and plasma are given.

© 2019 IEEE. One of the most effective methods of modeling of the vortical structures described by the 2-dimensional equation of carry of a vortex and by the Poisson equation for a flow function, namely, the contour dynamics (CD) method which is based on representation of a vortical stream by the finite area vortical regions is considered. The modification of the CD method minimizing the errors arising at its direct application to the description of vortical structures is offered.

© 2019 IEEE. On the basis of the analytical and numerical approaches the stability and dynamics of interaction of the multidimensional soliton-like solutions of the generalized nonlinear Schrödinger equation, which describes the waves in a plasma, fiber and planar optical waveguides, taking into account inhomogeneity and nonstationarity of propagation medium, is studied. The sufficient conditions of stability of the 2-dimensional and 3-dimensional solutions are obtained, and it is shown that even in the simplest 1-dimensional case the GNLS equation can have stable and quasi-stable solutions of the soliton and breather types and also unstable solutions which disperses with time. Obtained results can be useful in numerous applications in plasma physics, nonlinear optics and in many other fields of physics.

© 2019 IEEE. The results of theoretical and numerical study of the structure and dynamics of 2D and 3D solitons and nonlinear waves described by Kadomtsev-Petviashvili, 3-DNLS classes of equations and also the vortex systems described by Euler-type equations are presented. The generalizations (relevant to various complex physical media), accounting for high-order dispersion corrections, dissipation, instabilities, and stochastic fluctuations of the wave fields are considered. Special attention is paid to the applications of the theory in different fields of modern physics including plasma physics, hydrodynamics and physics of the upper atmosphere.

© 2019 IEEE. The results of simulation of evolution and interaction of the multidimensional soliton structures being described by the equations of nonlinear BK system, namely: generalized KP equation, 3-DNLS and 3-GNLS equations are presented. It is shown that the collision interaction can be elastic and non-elastic with the N-soliton structures' formation. The results are in conformity with the stability conditions obtained earlier analytically for the equations of the BK system.

© 2018, Pleiades Publishing, Ltd. An analytical solution of direct and inverse problems arising in the study of the internal gravity waves (IGWs) dynamic via recording of the Doppler frequency shift, is presented. The direct problem is to determine the response of the Doppler shift to IGWs in the region of the radio wave reflection point; the inverse problem is the determination of IGW parameters from data on the Doppler frequency shift. Solutions were obtained in an approximation of the isothermal ionosphere for the heights of the F-region. They are presented in a form convenient for their practical use and can have a wide range of applications, including the detection of soliton-like wave structures in the F-region of the ionosphere.

We propose a criterion for estimating the experimentally obtained time series for stationarity. The criterion makes it possible to automatically choose in real time the corresponding process of further processing and analyzing the recorded information and, correspondingly, improve reliability of the spectral estimates of a signal. The step-by-step estimation algorithm is presented. © 2013 Springer Science+Business Media New York.

We present an algorithm for finding the electromagnetic field produced by an antenna located near a semiconducting plane by the method of images. The results of calculating the radiation pattern of an X-shaped antenna system with four inclined beams, which is located in immediate proximity of the Earth's surface, are presented. © 2014 Springer Science+Business Media New York.

© 2015 Elsevier Ltd. The nonlinear dynamics of the 3D solitary Alfvén waves propagating nearly parallel to the external magnetic field in plasma of ionosphere and magnetosphere, which are described by the model of the 3-DNLS equation, is studied analytically and numerically. Under the assumption of negligible dissipative effects the analytical estimates and the sufficient conditions for the stability of 3D solutions of the 3-DNLS equation are obtained, based on the transformational properties of the system's Hamiltonian for the whole range of the equation coefficients. On the basis of asymptotic analysis the solutions asymptotics are presented. To study the evolution of the 3D Alfvén solitary waves including propagation of the Alfvén waves' beams in a magnetized plasma the equation are integrated numerically using the simulation codes specially developed. The results show that the 3-DNLS equation in non-dissipative case can have the stable 3D solutions in form of the 3D Alfvén solitons, and also on a level with them the 3D solutions collapsing or dispersing with time. In terms of the self-focusing phenomenon the results obtained can be interpreted as the formation of the stationary Alfvén wave beam propagating nearly parallel to magnetic field, or Alfvén wave beam spreading, or the self-focusing of the Alfvén wave beam. The influence of the dissipation in the medium on structure and character of evolution of 3D Alfvén waves is studied.

© 2014 IEEE. The mobile experimental complex was created by the authors for research of the electromagnetic (EM) fields generated by the electrical equipment and the elements of electric power systems in a wide frequency range. The description of the architecture and composition of the equipment is given, and its functionalities are considered. The complex is used to monitor the EM environment of objects for the purpose of solving of problems of electromagnetic compatibility (EMC). The results of monitor studies of the EM environment at two energy and industry sites are given.

© 2015 COSPAR. Published by Elsevier Ltd. All rights reserved. The dynamics of the 2D solitary nonlinear internal gravity waves (IGW), as well as traveling ionospheric disturbances (TID) of the electron density excited by them at heights of the ionosphere F-region, for conditions close to those of the F-layer assuming that the source of initial perturbation has the pulse character is studied analytically and numerically. On a level with general case the rather interesting applications when the sharp gradients of the ionospheric parameters are the functions of space coordinates and time, namely the IGW and TID dynamics in the frontal regions of the solar terminator and solar eclipse are considered. The results obtained describe the dynamical structure, evolution and transformation of the IGW and TID at heights of the ionosphere F-layer including its strongly heterogeneous regions.

© 2017 COSPAR The results of analysis and numerical simulation of evolution and interaction of the N-vortex structures of various configuration and different vorticities in the continuum including atmosphere, hydrosphere and plasma are presented. It is found that in dependence on initial conditions the regimes of weak interaction with quasi-stationary evolution and active interaction with the “phase intermixing”, when the evolution can lead to formation of complex forms of vorticity regions, are realized in the N-vortex systems. For the 2-vortex interaction the generalized critical parameter determining qualitative character of interaction of vortices is introduced. It is shown that for given initial conditions its value divides modes of active interaction and quasi-stationary evolution. The results of simulation of evolution and interaction of the two-dimensional and three-dimensional vortex structures, including such phenomena as dynamics of the atmospheric synoptic vortices of cyclonic types and tornado, hydrodynamic 4-vortex interaction and also interaction in the systems of a type of “hydrodynamic vortex – dust particles” are presented. The applications of undertaken approach to the problems of such plasma systems as streams of charged particles in a uniform magnetic field B and plasma clouds in the ionosphere are considered. It is shown that the results obtained have obvious applications in studies of the dynamics of the vortex structures dynamics in atmosphere, hydrosphere and plasma.

© 2017, Pleiades Publishing, Ltd. The structure and dynamics of ion-acoustic waves in an unmagnetized plasma, including the case of weakly relativistic collisional plasma (when it is necessary to take into account the high energy particle flows which are observed in the magnetospheric plasma), are studied analytically and numerically on the basis of a model of the Kadomtsev-Petviashvili (KP) equation. It is shown that, if the velocity of plasma particles approaches the speed of light, the relativistic effects start to strongly influence on the wave characteristics, such as its phase velocity, amplitude, and characteristic wavelength, with the propagation of the twodimensional solitary ion-acoustic wave. The results can be used in the study of nonlinear wave processes in the magnetosphere and in laser and astrophysical plasma.

© 2017 COSPAR The results of analysis and numerical simulation of evolution and interaction of the N-vortex structures of various configuration and different vorticities in the continuum including atmosphere, hydrosphere and plasma are presented. It is found that in dependence on initial conditions the regimes of weak interaction with quasi-stationary evolution and active interaction with the “phase intermixing”, when the evolution can lead to formation of complex forms of vorticity regions, are realized in the N-vortex systems. For the 2-vortex interaction the generalized critical parameter determining qualitative character of interaction of vortices is introduced. It is shown that for given initial conditions its value divides modes of active interaction and quasi-stationary evolution. The results of simulation of evolution and interaction of the two-dimensional and three-dimensional vortex structures, including such phenomena as dynamics of the atmospheric synoptic vortices of cyclonic types and tornado, hydrodynamic 4-vortex interaction and also interaction in the systems of a type of “hydrodynamic vortex – dust particles” are presented. The applications of undertaken approach to the problems of such plasma systems as streams of charged particles in a uniform magnetic field B and plasma clouds in the ionosphere are considered. It is shown that the results obtained have obvious applications in studies of the dynamics of the vortex structures dynamics in atmosphere, hydrosphere and plasma.

© 2017, Pleiades Publishing, Ltd. The structure and dynamics of ion-acoustic waves in an unmagnetized plasma, including the case of weakly relativistic collisional plasma (when it is necessary to take into account the high energy particle flows which are observed in the magnetospheric plasma), are studied analytically and numerically on the basis of a model of the Kadomtsev-Petviashvili (KP) equation. It is shown that, if the velocity of plasma particles approaches the speed of light, the relativistic effects start to strongly influence on the wave characteristics, such as its phase velocity, amplitude, and characteristic wavelength, with the propagation of the twodimensional solitary ion-acoustic wave. The results can be used in the study of nonlinear wave processes in the magnetosphere and in laser and astrophysical plasma.

© 2015 Elsevier Ltd. The nonlinear dynamics of the 3D solitary Alfvén waves propagating nearly parallel to the external magnetic field in plasma of ionosphere and magnetosphere, which are described by the model of the 3-DNLS equation, is studied analytically and numerically. Under the assumption of negligible dissipative effects the analytical estimates and the sufficient conditions for the stability of 3D solutions of the 3-DNLS equation are obtained, based on the transformational properties of the system's Hamiltonian for the whole range of the equation coefficients. On the basis of asymptotic analysis the solutions asymptotics are presented. To study the evolution of the 3D Alfvén solitary waves including propagation of the Alfvén waves' beams in a magnetized plasma the equation are integrated numerically using the simulation codes specially developed. The results show that the 3-DNLS equation in non-dissipative case can have the stable 3D solutions in form of the 3D Alfvén solitons, and also on a level with them the 3D solutions collapsing or dispersing with time. In terms of the self-focusing phenomenon the results obtained can be interpreted as the formation of the stationary Alfvén wave beam propagating nearly parallel to magnetic field, or Alfvén wave beam spreading, or the self-focusing of the Alfvén wave beam. The influence of the dissipation in the medium on structure and character of evolution of 3D Alfvén waves is studied.

© 2015 COSPAR. Published by Elsevier Ltd. All rights reserved. The dynamics of the 2D solitary nonlinear internal gravity waves (IGW), as well as traveling ionospheric disturbances (TID) of the electron density excited by them at heights of the ionosphere F-region, for conditions close to those of the F-layer assuming that the source of initial perturbation has the pulse character is studied analytically and numerically. On a level with general case the rather interesting applications when the sharp gradients of the ionospheric parameters are the functions of space coordinates and time, namely the IGW and TID dynamics in the frontal regions of the solar terminator and solar eclipse are considered. The results obtained describe the dynamical structure, evolution and transformation of the IGW and TID at heights of the ionosphere F-layer including its strongly heterogeneous regions.

© 2014 IEEE. The mobile experimental complex was created by the authors for research of the electromagnetic (EM) fields generated by the electrical equipment and the elements of electric power systems in a wide frequency range. The description of the architecture and composition of the equipment is given, and its functionalities are considered. The complex is used to monitor the EM environment of objects for the purpose of solving of problems of electromagnetic compatibility (EMC). The results of monitor studies of the EM environment at two energy and industry sites are given.

We propose a criterion for estimating the experimentally obtained time series for stationarity. The criterion makes it possible to automatically choose in real time the corresponding process of further processing and analyzing the recorded information and, correspondingly, improve reliability of the spectral estimates of a signal. The step-by-step estimation algorithm is presented. © 2013 Springer Science+Business Media New York.