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Study of the Kernels of Integral Equations in Problems of Wave Diffraction in Waveguides and by Periodic Structures

  • INTEGRAL AND INTEGRO-DIFFERENTIAL EQUATIONS
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Abstract

We consider the problem of diffraction of a waveguide wave by an impedance rod in a rectangular waveguide with perfectly conducting walls and the problem of diffraction of a plane two-dimensional electromagnetic wave and the field of a point source by an evenly spaced array formed by infinite cylinders of arbitrary cross-section with perfectly and well conducting walls. Both problems are reduced to solving contour Fredholm integral equations. Such reduction is based on using the Green’s function of an empty planar waveguide and a quasiperiodic Green’s function, which are infinite series in the eigenfunctions of the cross-section of the planar waveguide and in the eigenfunctions satisfying the Floquet conditions. To calculate the kernels of the resulting integral equations, depending on both the Green’s functions themselves and their derivatives, we have developed special algorithms to improve the convergence of the series and explicitly isolate the logarithmic singularity occurring in the series.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, 119991, Russia

    A. S. Il’inskii & T. N. Galishnikova

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  1. A. S. Il’inskii
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  2. T. N. Galishnikova
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Correspondence to A. S. Il’inskii or T. N. Galishnikova.

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Translated by V. Potapchouck

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Il’inskii, A.S., Galishnikova, T.N. Study of the Kernels of Integral Equations in Problems of Wave Diffraction in Waveguides and by Periodic Structures. Diff Equat 56, 1167–1180 (2020). https://doi.org/10.1134/S0012266120090074

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  • DOI: https://doi.org/10.1134/S0012266120090074

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