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The propagation of TE-polarized electromagnetic waves along a Kerr-type nonlinear dielectric, nonabsorbing, nonmagnetic, and isotropic (circular) cylindrical waveguide is investigated. For axially (azimuthal) symmetric solutions the problem is reduced to a cubic-nonlinear integral equation that is solved by iteration leading to a sequence uniformly… (More)
The problem of diffraction of an electromagnetic field by a locally nonhomogeneous body in a perfectly conducting waveguide of rectangular cross section is considered. This problem is reduced to solving a volume singular integral equation (VSIE). The examination of this equation is based on the analysis of the corresponding boundary value problem (BVP) for… (More)
The creation and justification of the methods for minimax estimation of parameters of the external boundary value problems for the Helmholtz equation in unbounded domains are considered. When observations are distributed in subdomains, the determination of minimax estimates is reduced to the solution of integro-differential equations in bounded domains.… (More)
It is shown that the transmission coefficient of parallel-plane multi-sectional dielectric diaphragms in a waveguide of rectangular cross section has singularities in the complex plane of the longitudinal wavenumber of each section and the singularities are associated with resonant states of the transmission problem.
We consider numerical determination of the dielectric media parameters of inclusions in a waveguide of rectangular cross-section from the transmission coefficient. We develop and apply computer codes implementing the FDTD algorithm for nonstationary Maxwell's equations with perfectly matched layer (PML) absorbing boundary conditions using the Berenger… (More)
This study was partially supported by the project granted by Teknikbrostiftelsen, Gothenburg, Sweden (2002). The purpose of the project was to create non-standard codes, tools, and facilities together with the written materials (compendiums, textbooks) in order to simplify and improve teaching of applied and numerical mathematics so that the teachers and… (More)
The analysis is performed and theorems are formulated concerning general form of guaranteed estimates of linear functionals from unknown data of Helmholtz transmission problems arising in electromagnetics and acoustics of inhomogeneous dielectric media.
We investigate the estimation problems of linear functionals from solutions to transmission problems for Helmholtz equation with inexact data. The right-hand sides of equations entering the statements of transmission problems and the statistical characteristics of observations errors are supposed to be unknown and belonging to the certain sets. It is shown… (More)
We give a general description of mathematical background and a resume of the results about existence and distribution of the spectra of running waves in open waveguides, including metal-dielectric waveguides with arbitrary cylindrical in-homogeneities, layered concentric dielectric waveguides of circular cross section and Goubau lines with layered… (More)
This work is devoted to the development of a numerical-analytical method for solving the inverse problem of reconstructing tensor permittivity of a multi-sectional diaphragm in a rectangular waveguide. Numerical results are presented that confirm the efficiency of the proposed technique.