A nonlinear eigenvalueproblem for a system of three equations with boundary conditions of the first kind, describing the propagation of electromagnetic waves in a plane nonlinear waveguide, is considered. This is a t...
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A nonlinear eigenvalueproblem for a system of three equations with boundary conditions of the first kind, describing the propagation of electromagnetic waves in a plane nonlinear waveguide, is considered. This is a two-parameterproblem with one spectral parameter and a second parameter arising from an additional condition. This condition connects the integration constants that arise when finding the first integrals of the system. The existence of nonlinearizable solutions of the problem is proved.
Propagation of the coupled electromagnetic wave, which is a superposition of TE surface and TM leaky waves, in the Goubau line (a perfectly conducting cylinder covered by a concentric dielectric layer) filled with non...
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Propagation of the coupled electromagnetic wave, which is a superposition of TE surface and TM leaky waves, in the Goubau line (a perfectly conducting cylinder covered by a concentric dielectric layer) filled with nonlinear inhomogeneous medium is studied (if the permittivity is linear, the coupled wave does not exist). Nonlinear coupled TE-TM wave is characterised by two (independent) frequencies and two (coupled) propagation constants (propagation constants). The physical problem is reduced to a nonlinear two-parameter transmission eigenvalueproblem for Maxwell's equations. Existence of coupled TE-TM waves is proved. Intervals of localisation of propagation constants are found.
The propagation of monochromatic nonlinear symmetric hybrid surface waves in a cylindrical nonlinear anisotropic inhomogeneous metal-dielectric waveguide is considered. The physical problem is reduced to solving a tra...
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The propagation of monochromatic nonlinear symmetric hybrid surface waves in a cylindrical nonlinear anisotropic inhomogeneous metal-dielectric waveguide is considered. The physical problem is reduced to solving a transmission eigenvalueproblem for a system of ordinary differential equations. Spectral parameters of the problem are propagation constants of the waveguide. The setting is reduced to a new type of nonlinear eigenvalueproblem and an analytical method of its solution is developed. The propagation modes are found that have not been previously reported in the literature. 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.
Paper focuses on the propagation of monochromatic nonlinear symmetric hybrid waves in a planar dielectric waveguide filled with nonlinear medium. The wave propagation problem is reduced to a transmission eigenvalue pr...
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Paper focuses on the propagation of monochromatic nonlinear symmetric hybrid waves in a planar dielectric waveguide filled with nonlinear medium. The wave propagation problem is reduced to a transmission eigenvalueproblem. eigenvalues of the problem depend on an additional parameter and correspond to propagation constant. Using perturbation method, it is theoretically proved the existence of a finite number of isolated eigenvalues and therefore, guide waves. The found guide regime is novel in the theory of nonlinear waveguides. Numerical results are presented.
The model eigenvalueproblem , w(-1)?=?w(1)?=?0, contains two complex parameters E and z. Considering E as a function of z one obtains a spectral Riemann surface. Level crossings between sheets of the spectral surface...
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The model eigenvalueproblem , w(-1)?=?w(1)?=?0, contains two complex parameters E and z. Considering E as a function of z one obtains a spectral Riemann surface. Level crossings between sheets of the spectral surface are given explicitly, and the existence of a double sequence of branch points is proved.
Given a quadratic two-parameter matrix polynomial Q(?,?mu), we develop a systematic approach to generating a vector space of linear two-parameter matrix polynomials. The purpose for constructing this vector space is t...
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Given a quadratic two-parameter matrix polynomial Q(?,?mu), we develop a systematic approach to generating a vector space of linear two-parameter matrix polynomials. The purpose for constructing this vector space is that potential linearizations of Q(?,?mu) lie in it. Then, we identify a set of linearizations and describe their constructions. Finally, we determine a class of linearizations for a quadratic two-parameter eigenvalue problem.
The article deals with the problem of propagation of a two-frequency electromagnetic wave in a waveguide filled with a nonlinear medium. A two-frequency wave is the sum of two monochromatic TE waves with different fre...
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The article deals with the problem of propagation of a two-frequency electromagnetic wave in a waveguide filled with a nonlinear medium. A two-frequency wave is the sum of two monochromatic TE waves with different frequencies. The permittivity of the waveguide is characterized by a very general nonlinearity function corresponding to self-action effects. It is shown that, under certain conditions, the two-frequency wave is an eigenmode of the waveguide. From a mathematical point of view, the problem reduces to a nonlinear two-parameter eigenvalue problem for the system of (nonlinear) Maxwell's equations. The main result of the article is the proof of the existence of nonlinearizable solutions of the problem.
The problem of building a numerical algorithm for determination of branching points of one nonlinear integral operator, which arises in the theory of antennas synthesis according to the given amplitude radiation patte...
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ISBN:
(纸本)0780378814
The problem of building a numerical algorithm for determination of branching points of one nonlinear integral operator, which arises in the theory of antennas synthesis according to the given amplitude radiation pattern, is considered. The basic difficulty, consists in that the kernel of an integral operator nonlinearly depends oil twoparameters, which play role of the spectral ones. For such problems, except a special case. the existing numerical algorithms are not applicable. For building an algorithm for solving such problems, the equivalent variational statement is used. The problem is reduced to a sequence of linear two-parameter eigenvalue problems with application of one gradient procedure for simultaneous evaluation of two spectral parameters being the branching points of an initial nonlinear integral operator.
Paper focuses on the propagation of monochromatic nonlinear symmetric hybrid waves in a planar dielectric waveguide filled with nonlinear anisotropic medium. The wave propagation problem is reduced to a transmission e...
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Paper focuses on the propagation of monochromatic nonlinear symmetric hybrid waves in a planar dielectric waveguide filled with nonlinear anisotropic medium. The wave propagation problem is reduced to a transmission eigenvalueproblem. eigenvalues of the problem depend on an additional parameter and correspond to propagation constant. Using a perturbation method, it is theoretically proved the existence of a finite number of isolated eigenvalues and, therefore, guide waves. Numerical results are presented.
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