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  • 1.
    Medvedik, M. Y.
    et al.
    Department of mathematics and supercomputing, Penza State University, Penza, Russia.
    Smirnov, Yu. G.
    Department of mathematics and supercomputing, Penza State University, Penza, Russia.
    Smolkin, Eugene Yu.
    University of Gävle, Faculty of Engineering and Sustainable Development.
    Tsupak, Aleksei A.
    Department of mathematics and supercomputing, Penza State University, Penza, Russia.
    Electromagnetic wave diffraction by a system of non-intersecting obstacles of various dimensions2015In: Proceedings of the 2015 International Conference on Electromagnetics in Advanced Applications: ICEAA 2015, 2015, p. 1568-1571Conference paper (Refereed)
    Abstract [en]

    The vector problem of time-harmonic electromagnetic wave diffraction by a system of non-intersecting solid inhomogeneous bodies, infinitely thin perfectly conducting screens and wire antennas is considered. The original boundary value problem for Maxwell’s equations is reduced to a system of integro-differential equations over the volume domains, the screen surfaces and antennas. To solve the integral equations approximately, the Bubnov-Galerkin method is applied; basis functions on the body, the screens and antennas are introduced as well as formulas for matrix elements in the Galerkin method. To solve the problem of diffraction by obstacles of complex shape, the subhierarchical approach is applied. © 2015 IEEE.

  • 2.
    Shestopalov, Yury
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Smirnov, Yury
    Penza State University, Penza, Ryssland.
    Smolkin, Eugene
    Penza State University, Russia.
    New Propagation Regimes of Symmetric Hybrid Waves in a Nonlinear Metal-Dielectric Waveguide2018In: IET Conference Publications 2018, Piscataway, New Jersey, USA: IEEE, 2018, Vol. CP741, article id 1570402136Conference paper (Refereed)
    Abstract [en]

    The propagation of monochromatic nonlinear symmetric hybrid waves in a cylindrical nonlinear metal-dielectric waveguide is considered. The physical setting is reduced to a transmission eigenvalue problem for a system of ordinary differential equations which is new type of nonlinear eigenvalue problem where spectral parameters are the wave propagation constants. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

  • 3.
    Shestopalov, Yury
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Smolkin, Eugene
    Penza State University, Russia.
    Kuzmina, Ekaterina
    Moscow Technologiical University MIREA, Moscow, Russia.
    Spectra of Nonselfadjoint Eigenvalue Problems for Elliptic Systems in Mathematical Models of the Wave Propagation in Open Waveguides2018In: Lobachevskii Journal of Mathematics, ISSN 1995-0802, E-ISSN 1818-9962, Vol. 39, no 8, p. 1117-1129Article in journal (Refereed)
    Abstract [en]

    Statements and analysis are presented of nonselfadjoint eigenvalue problems for ellipticequations and systems, including singular Sturm–Liouville problems on the line, that arise inmathematical models of the wave propagation in open metal-dielectric waveguides. Existence ofreal and complex spectra are proved and their distribution is investigated for canonical structurespossessing circular symmetry of boundary contours.

  • 4.
    Shestopalov, Yury
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
    Smolkin, Eugene
    Smirnov, Yury
    Department of Mathematics and Supercomputing, Penza State University, Krasnaya Str. 40, Penza, 440026, Russia.
    On the existence of the nonlinear leaky TE-polarized waves in a metal–dielectric cylindrical waveguide2019In: Wave motion, ISSN 0165-2125, E-ISSN 1878-433X, Vol. 91, article id 102378Article in journal (Refereed)
    Abstract [en]

    We consider propagation of leaky waves in the Goubau line (a perfectly conducting cylinder covered by a concentric dielectric layer) filled with nonlinear inhomogeneous medium. The problem is reduced to the analysis of a nonlinear integral equation with a kernel in the form of the Green’s function of an auxiliary boundary value problem on an interval. The existence of propagating nonlinear leaky waves for the chosen nonlinearity (Kerr law) is proved using the method of contraction. Conditions under which a finite number of waves can propagate are obtained and the intervals of localization of the corresponding propagation constants are determined. For the numerical solution, a method based on solving an auxiliary Cauchy problem (a version of the shooting method) is proposed. In numerical experiments, two types of nonlinearities are considered and compared: Kerr nonlinearity and nonlinearity with saturation. New propagation regimes are discovered.

  • 5.
    Shestopalov, Yury
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Smolkin, Eugene
    Department of Mathematics and Supercomputing, Penza State University, Penza, Russia.
    Snegur, M.
    Department of Mathematics and Supercomputing, Penza State University, Penza, Russia.
    TE-polarized Wave Diffraction by a Cylinder Covered with Nonlinear Dielectric Layer2018In: Proceedings of 2018 IEEE Asia-Pacific Conference on Antennas and Propagation (APCAP), 2018, p. 321-322Conference paper (Refereed)
    Abstract [en]

    The problem of diffraction of TE polarized EM waves by an open dielectric waveguide with a nonlinear inhomogeneous filling is under consideration. In such problems a nonlinear eigenvalue problem for a system of differential equations is arised. For the numerical solution a method based on the solution of the auxillary Cauchy problem is proposed. Numerical results are presented.

  • 6.
    Shestopalov, Yury
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
    Smolkin, Eugene
    Department of Mathematics and Supercomputing, Penza State University, Penza, Russia.
    Snegur, Maxim
    Department of Mathematics and Supercomputing, Penza State University, Penza, Russi.
    New Propagation Regimes of TE Waves in a Waveguide filled with a Nonlinear Dielectric Metamaterial2019In: 2019 URSI Asia-Pacific Radio Science Conference (AP-RASC), New Dehli: IEEE, 2019, article id 8738241Conference paper (Refereed)
    Abstract [en]

    We consider propagation of surface TE waves in a circular metal-dielectric waveguide filled with nonlinear (Kerr nonlinearity) metamaterial medium. Analysis is reduced to solving a nonlinear transmission eigenvalue problem for an ordinary differential equation; eigenvalues of the problem correspond to propagation constants of the waveguide. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

  • 7.
    Shestopalov, Yury
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Smolkin, Eugene
    Penza State University, Russia.
    Snegur, Maxim
    Penza State University, Russia.
    Numerical Study of Multilayer Nonlinear Inhomogeneous Goubau Lines2018In: Proceedings of the 2018 International Conference on Electromagnetics in Advanced Application (ICEAA), Piscataway, New Jersey, USA: IEEE conference proceedings, 2018, p. 126-129, article id 8520464Conference paper (Refereed)
    Abstract [en]

    We consider propagation of surface TE waves in a circular metal-dielectric waveguide filled with nonlinear (Kerr nonlinearity) multilayered inhomogeneous medium. Analysis is reduced to solving a nonlinear transmission eigenvalue problem for an ordinary differential equation; eigenvalues of the problem correspond to propagation constants of the waveguide. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

  • 8.
    Smirnov, Yuri
    et al.
    Department of Mathematics and Supercomputing, Penza State University, Russian Federation.
    Smolkin, Eugene
    Department of Mathematics and Supercomputing, Penza State University, Russian Federation.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
    Diffraction of a TE-Polarized Wave by a Nonlinear Goubau Line2019In: Radio Science, ISSN 0048-6604, E-ISSN 1944-799X, Vol. 54, no 1, p. 151-157Article in journal (Refereed)
    Abstract [en]

    The diffraction of a cylindrical wave by a nonlinear metal-dielectric waveguide filled with nonlinear medium is considered. Two widely used types of nonlinearities (Kerr nonlinearity and nonlinearity with saturation) are considered. The problem is to find amplitudes of the reflected and the transmitted fields when the amplitude of the incident field is known. The analytical and numerical solution techniques are developed. Numerical results are presented. ©2019. American Geophysical Union. All Rights Reserved.

  • 9.
    Smirnov, Yury
    et al.
    Department of Mathematics and Supercomputing, Penza State University, Penza, Russia.
    Smolkin, Eugene
    Department of Mathematics and Supercomputing, Penza State University, Penza, Russia.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    On the existence of non-polarized azimuthal-symmetric electromagnetic waves in circular metal-dielectric waveguide filled with nonlinear radially inhomogeneous medium2018In: Journal Electromagnetic Waves and Applications, ISSN 0920-5071, E-ISSN 1569-3937, Vol. 32, no 11, p. 1389-1408Article in journal (Refereed)
    Abstract [en]

    Propagation of monochromatic nonlinear symmetric hybrid waves in a cylindrical nonlinear inhomogeneous metal–dielectric waveguide is considered. The physical problem is reduced to solving a transmission eigenvalue problem for a system of ordinary differential equations where spectral parameters are the wave propagation constants. The setting under study is reduced to a new type of nonlinear eigenvalue problem. An analytical method for solving this problem is elaborated. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

  • 10.
    Smolkin, Eugene
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Goubau line filled with nonlinear medium: Numerical study of TM-polarized waves2015In: Proceedings of the 2015 International Conference on Electromagnetics in Advanced Applications: ICEAA 2015, IEEE Press, 2015, p. 1572-1575Conference paper (Refereed)
    Abstract [en]

    The propagation of monochromatic electromagnetic TM waves in the Goubau line (conducting cylinder covered by a concentric dielectric layer) filled with nonlinear inhomogeneous medium is considered. Two types of nonlinearity are studied. A physical problem is reduced to solving a nonlinear transmission eigenvalue problem for a system of ordinary differential equations. Eigenvalues of the problem correspond to propagation constants of the waveguide. A method is proposed for finding approximate eigenvalues of the nonlinear problem based on solving an auxiliary Cauchy problem (by the shooting method). The existence of eigenvalues that correspond to a new propagation regime is predicted. A comparison with the linear case is given.

  • 11.
    Smolkin, Eugene
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Numerical method for electromagnetic wave propagation problem in a cylindrical anisotropic inhomogeneous metal-dielectric waveguide2017In: Progress in Electromagnetics Research Symposium, Electromagnetics Academy , 2017, p. 3201-3208Conference paper (Refereed)
    Abstract [en]

    The propagation of monochromatic electromagnetic waves in a cylindrical anisotropic metal-dielectric waveguide is considered. The physical problem is reduced to solving a transmission eigenvalue problem for a system of ordinary differential equations. Spectral parameters of the problem are propagation constants of the waveguide. Numerical results are found with a projection method.

  • 12.
    Smolkin, Eugene
    Penza State University, Penza, Russian Federation.
    Numerical Method for Electromagnetic Wave Propagation Problem in a Cylindrical Inhomogeneous Metal Dielectric Waveguiding Structures2017In: Mathematical Modelling and Analysis, ISSN 1392-6292, E-ISSN 1648-3510, Vol. 22, no 3, p. 271-282Article in journal (Refereed)
    Abstract [en]

    The propagation of monochromatic electromagnetic waves in metal circular cylindrical dielectric waveguides filled with inhomogeneous medium is considered. The physical problem is reduced to solving a transmission eigenvalue problem for a system of ordinary differential equations. Spectral parameters of the problem are propagation constants of the waveguide. Numerical results are found with a projection method. The comparison with known exact solutions (for particular values of parameters) is made.

  • 13.
    Smolkin, Eugene
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    The azimuthal symmetric hybrid waves in nonlinear cylindrical waveguide2017In: Progress in Electromagnetics Research Symposium, Electromagnetics Academy , 2017, p. 348-353Conference paper (Refereed)
    Abstract [en]

    The propagation of monochromatic nonlinear symmetric hybrid waves in a cylindrical nonlinear dielectric waveguide is considered. The physical problem is reduced to solving a transmission eigenvalue problem for a system of ordinary differential equations. Spectral parameters of the problem are propagation constants of the waveguide. Numerical results are found with the modification of the shooting method. The method allows us to determine approximate eigenvalues with any prescribed accuracy. The comparison with known exact solutions (for particular values of parameters) are made. The approach described in this paper can be applied to other problems, e.g., to multilayered inhomogeneous waveguides.

  • 14.
    Smolkin, Eugene
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Nonlinear Goubau line: analytical-numerical approaches and new propagation regimes2017In: Journal Electromagnetic Waves and Applications, ISSN 0920-5071, E-ISSN 1569-3937, Vol. 31, no 8, p. 781-797Article in journal (Refereed)
    Abstract [en]

    We consider propagation of surface TE waves in the Goubau line (GL) assuming that the dielectric cover is non-linear and inhomogeneous. The problem at hand is reduced to a non-linear integral equation with a kernel in the form of the Green function of an auxiliary boundary value problem on an interval. The existence of propagating TE waves for the chosen nonlinearity (Kerr law) is proved by the method of contraction. Conditions under which several higher-order waves can propagate are obtained, and the intervals of the corresponding propagation constants are determined. For the numerical solution, a method based on solving an auxiliary Cauchy problem (a version of the shooting method) is proposed. In numerical experiment two types of nonlinearities are considered and compared: Kerr nonlinearity and nonlinearity with saturation. New propagation modes are found.

  • 15.
    Smolkin, Eugene
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Numerical study of multilayered nonlinear inhomogeneous waveguides in the case of TE polarization2016In: 2016 10th European Conference on Antennas and Propagation: EuCAP 2016, Institute of Electrical and Electronics Engineers (IEEE), 2016, article id 7481782Conference paper (Refereed)
    Abstract [en]

    We consider propagation of surface TE waves in a circular dielectric waveguide filled with nonlinear (Kerr non-linearity) multilayered inhomogeneous medium. Each layer is characterized by a specific value of the nonlinearity coefficient α. Analysis is reduced to solving a nonlinear transmission eigenvalue problem for an ordinary differential equation; eigenvalues of the problem correspond to propagation constants of the waveguide. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

  • 16.
    Smolkin, Eugene
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Numerical study of multilayered nonlinear inhomogeneous waveguides in the case of TM polarization2016In: 2016 URSI International Symposium on Electromagnetic Theory (EMTS), IEEE conference proceedings, 2016, p. 247-250Conference paper (Refereed)
    Abstract [en]

    We consider propagation of surface TM waves in a circular dielectric waveguide filled with nonlinear (Kerr nonlinearity) multilayered inhomogeneous medium. Each layer is characterized by a specific value of the nonlinearity coefficient α. Analysis is reduced to solving a nonlinear transmission eigenvalue problem for an ordinary differential equation; eigenvalues of the problem correspond to propagation constants of the waveguide. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

  • 17.
    Smolkin, Eugene
    et al.
    Penza State University, Penza, Russia.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Snegur, Maxim
    Penza State University, Penza, Russia.
    Diffraction of TM polarized electromagnetic waves by a nonlinear inhomogeneous metal-dielectric waveguide2017In: 2017 International Conference on Electromagnetics in Advanced Applications (ICEAA), 2017, p. 1288-1291, article id 8065508Conference paper (Refereed)
    Abstract [en]

    In this work, we consider the diffraction of TM waves by an open metal-dielectric waveguide, a Goubau line (GL), with a nonlinear inhomogeneous dielectric cover. Numerical experiments are carried out for the nonlinearity with saturation. The physical problem is reduced to solving a nonlinear boundary value problem for a system of ordinary differential equations. Numerical results are obtained using a modification of the shooting method which makes it possible to determine and plot the amplitude of the reflected field with respect to the amplitude of the incident field. Comparison between the nonlinear problem and the corresponding linear setting is performed.

  • 18.
    Smolkin, Eugene
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Shestopalov, Yury V.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Nonlinear coupled TE-TM waves in Goubau line2016In: Proceedings of the 2016 18th International Conference on Electromagnetics in Advanced Applications, ICEAA 2016, 2016, p. 356-359, article id 7731397Conference paper (Refereed)
    Abstract [en]

    Nonlinear coupled electromagnetic TE-TM wave propagation in the Goubau line (a conducting cylinder covered by a concentric dielectric layer) filled with nonlinear inhomogeneous medium is considered. Nonlinearity inside the GL is described by the Kerr law. The physical problem is reduced to a nonlinear two-parameter eigenvalue problem for a system of (nonlinear) ordinary differential equations. For the numerical solution, a method based on solving an auxiliary Cauchy problem (the shooting method) is proposed. The coupled TE-TM waves propagating in GL are determined numerically. Whether these mathematically predicted propagation regime really exist is a hypothesis that can be proved or disproved in an experiment.

  • 19.
    Smolkin, Eugene
    et al.
    Penza State University, Penza, Russia.
    Snegur, Maxim
    Penza State University, Penza, Russia.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Diffraction of TM Polarized EM Waves by a Nonlinear Inhomogeneous Dielectric Cylinder2018In: 2018 Progress in Electromagnetics Research Symposium (PIERS-Toyama), 2018, p. 66-70Conference paper (Refereed)
    Abstract [en]

    In this work, we consider the diffraction of TM waves by a nonlinear inhomogeneous dielectric cylinder. Numerical experiments are carried out for the nonlinearity with saturation. The physical problem is reduced to solving a nonlinear boundary value problem for a system of ordinary differential equations. Numerical results are obtained using a modification of the shooting method which makes it possible to determine and plot the amplitude of the reflected field with respect to the amplitude of the incident field. Comparison between the nonlinear problem and the corresponding linear setting is performed.

  • 20.
    Smolkin, Eugene
    et al.
    Penza State University, Penza, Russia.
    Snegur, Maxim
    Penza State University, Penza, Russia.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Nonlinear Hybrid Waves in a Cylindrical Anisotropic Metal-Dielectric Waveguide2018In: 2018 Progress in Electromagnetics Research Symposium (PIERS-Toyama), 2018, p. 1948-1954Conference paper (Refereed)
    Abstract [en]

    The propagation of hybrid waves in a cylindrical anisotropic nonlinear metal-dielectric waveguide is considered. The physical setting is reduced to a transmission eigenvalue problem for a system of ordinary differential equations which is new type of nonlinear eigenvalue problem where spectral parameters are the wave propagation constants. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

  • 21.
    Smolkin, Eugene
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Tsupak, A. A.
    Department of Mathematics and Supercomputing, Penza State University, Penza, Russian Federation.
    Galerkin method for solving scalar problems of diffraction by a partially shielded inhomogeneous body2016In: Proceedings of the 2016 18th International Conference on Electromagnetics in Advanced Applications, ICEAA 2016, 2016, p. 360-363, article id 7731398Conference paper (Refereed)
    Abstract [en]

    The scalar problem of diffraction by an inhomogeneous partially shielded body is considered. The boundary value problem leads to a system of integral equations on two- and three-dimensional manifolds with boundary. The equivalence of the integral and differential formulations of the problem is established; the Fredholm property and invertibility of the matrix operator are proved. Galerkin method for numerical solving of the integral equations is proposed. The approximation property for compactly supported basis functions as well as the convergence of Galerkin method in proper Sobolev spaces is proved. Numerical results are provided.

1 - 21 of 21
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