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Vekslerchik V.E.,Kharkov National University of Radio Electronics | Vekslerchik V.E.,University of Castilla - La Mancha
Nonlinearity | Year: 2011

This work is devoted to an integrable generalization of the nonlinear Schrödinger equation proposed by Fokas and Lenells. I discuss the relationships between this equation and other integrable models. Using the reduction of the Fokas-Lenells equation to the already known ones I obtain the N-dark soliton solutions. © 2011 IOP Publishing Ltd & London Mathematical Society.

Bodyanskiy Y.,Kharkov National University of Radio Electronics | Vynokurova O.,Kharkov National University of Radio Electronics
Information Sciences | Year: 2013

In the paper a five-layers architecture of hybrid wavelet-neuro-fuzzy system which is using the adaptive W-neurons as the nodes is proposed. W-neuron is a neuron which structure is similar to a radial basis functions network, but instead of conventional radial basis functions we used multidimensional adaptive wavelet activation-membership functions. The distinctive feature of the proposed system is usage of the wavelets as membership functions in the antecedent layer, and the adaptive multidimensional wavelets as activation functions in the consequent layer that can tune not only the dilation and translation parameters but also its own form during the learning process. The learning algorithms for all antecedent and consequent functions' parameters that have both following and filtering properties are proposed. The experimental results have shown that this wavelet-neuro-fuzzy system has improved approximation properties and has a higher learning rate in comparison with usual wavelet-neuro-fuzzy networks. The proposed hybrid wavelet-neuro-fuzzy system can be used to solve tasks of diagnosis, forecasting, emulation, and identification of nonlinear chaotic and stochastic non-stationary processes. © 2012 Elsevier Inc. All rights reserved.

Kozar A.I.,Kharkov National University of Radio Electronics
CriMiCo 2012 - 2012 22nd International Crimean Conference Microwave and Telecommunication Technology, Conference Proceedings | Year: 2012

Plotting of structure functions of electromagnetic interaction of electric and magnetic types for limited 3D orthogonal resonant gratings from small magnetodielectric spheres in the external homogeneous magnetodielectric environment is considered. © 2012 CriMiCo.

Stognii N.P.,Kharkov National University of Radio Electronics | Sakhnenko N.K.,Kharkov National University of Radio Electronics
IEEE Journal on Selected Topics in Quantum Electronics | Year: 2013

This paper presents a straightforward analysis of the plasmonic properties of metal wires arranged in a linear chain of a finite length. For this we solve eigenvalue problem in form of matrix equations that allow thorough investigation of plasmonic modes with different field distributions. Our modeling provides results in terms of eigen oscillating frequencies and quality factors with controllable accuracy. It has revealed the possibility of quality factor dramatic enhancement for certain plasmonic modes by adjusting the separation distances and increasing the number of wires in a chain. © 1995-2012 IEEE.

Kulagin N.A.,Kharkov National University of Radio Electronics
Journal of Luminescence | Year: 2011

Selected data of ab initio simulation of the electronic structure and spectral properties of either cluster with ions of iron, rare earth or actinium group elements have been presented here. Appearance of doped Cr+4 ions in oxides, Cu+2 in HTSC, Nd+2 in solids has been discussed. Analysis of experimental data for plasma created ordered structures of crystallites with size of about 10-9 m on surface of separate oxides are given, too. Change in the spectroscopic properties of clusters and nano-structures on surface of strontium titanate crystals discussed shortly using the X-ray line spectroscopy experimental results. © 2011 Elsevier B.V.

Vekslerchik V.E.,Kharkov National University of Radio Electronics
Journal of Physics A: Mathematical and Theoretical | Year: 2015

We present a set of bilinear matrix identities that generalize the ones that have been used to construct the bright soliton solutions for various models. As an example of an application of these identities, we present a simple derivation of the N-bright soliton solutions for the Ablowitz-Ladik hierarchy. © 2015 IOP Publishing Ltd.

Petrova S.A.,Kharkov National University of Radio Electronics
Astrophysical Journal | Year: 2013

The dipolar magnetic field structure of a neutron star is modified by the plasma originating in the pulsar magnetosphere. In the simplest case of a stationary axisymmetric force-free magnetosphere, a self-consistent description of the fields and currents is given by the well-known pulsar equation. Here we revise the commonly used boundary conditions of the problem in order to incorporate the plasma-producing gaps and to provide a framework for a truly self-consistent treatment of the pulsar magnetosphere. A generalized multipolar solution of the pulsar equation is found, which, as compared to the customary split monopole solution, is suggested to better represent the character of the dipolar force-free field at large distances. In particular, the outer gap location entirely inside the light cylinder implies that beyond the light cylinder the null and critical lines should be aligned and become parallel to the equator at a certain altitude. Our scheme of the pulsar force-free magnetosphere, which will hopefully be followed by extensive analytic and numerical studies, may have numerous implications for different fields of pulsar research. © 2013. The American Astronomical Society. All rights reserved..

Vekslerchik V.E.,Kharkov National University of Radio Electronics
Journal of Nonlinear Mathematical Physics | Year: 2013

This paper is devoted to the negative flows of the derivative nonlinear Schrödinger hierarchy (DNLSH). The main result of this work is the functional representation of the extended DNLSH, composed of both positive (classical) and negative flows. We derive a finite set of functional equations, constructed by means of the Miwa's shifts, which contains all equations of the hierarchy. Using the obtained functional representation we convert the nonlocal equations of the negative subhierarchy into local ones of higher order, derive the generating function of the conservation laws and the N-soliton solutions for the extended DNLSH under non-vanishing boundary conditions. Copyright: the authors.

Petrova S.A.,Kharkov National University of Radio Electronics
Monthly Notices of the Royal Astronomical Society | Year: 2014

The self-consistent two-fluid model of the pulsar magnetosphere is considered. We concentrate on the case of vanishingly small inertia of the particles. Our approach allows us to obtain the realistic particle distributions sustaining the force-free magnetic field configuration of a monopolar structure. The result differs substantially from the customary picture of the radial speed-of-light motion of massless particles. In our case, the electron and positron constituents follow slightly curved trajectories and are characterized by definite number densities and distinct velocities. The velocity shift is determined by the first-order longitudinal electric field, which appears to be the necessary ingredient of the self-consistent two-fluid model and implies the parallel conductivity of the order of the inverse particle mass. Our model is believed to be a proper context to describe radiation processes in the pulsar magnetosphere, including both the radio and high-energy emissions. The velocity shift is suggestive of the two-stream instability which may underlie the pulsar radio emission mechanism. The differential rotation of the particle flow may cause the diochotron instability expected to be responsible for the radio subpulse phenomenon. The connection between the radio and high-energy emissions of pulsars is predicted as well. © 2014 The Author.

Petrova S.A.,Kharkov National University of Radio Electronics
Monthly Notices of the Royal Astronomical Society | Year: 2012

The stationary axisymmetric force-free magnetosphere of a pulsar is studied analytically. The pulsar equation is solved in the region close to the magnetic axis. Proceeding from the linearization of the current function in the axial region, we find an axial magnetic flux function valid at any altitude above the neutron star. This function is used as a starting approximation to develop series for the non-linear pulsar equation in the polar region. Taking into account the quasi-monopolar character of the pulsar magnetic flux at infinity, we obtain unique asymptotic series for the flux and current functions. At infinity, both functions are close but not equivalent to those known for the case of a force-free monopole. The flux function at the top of the polar gap is found to differ from the dipolar one at the neutron star surface. With our results, the transverse current sheet closing the pulsar circuit at the neutron star surface is consistently incorporated into the global magnetospheric structure, backward particle flow at small polar angles can be excluded and the stationary cascade scenario looks admissible. The present paper is the first step towards a complete analytic description of the pulsar force-free magnetosphere allowing for plasma-producing gaps and pulsar current circuit closure. © 2012 The Author Monthly Notices of the Royal Astronomical Society. © 2012 RAS.

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