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Mathematics

The problem of propagation of electromagnetic waves in a layer with arbitrary nonlinearity (II. TM waves)

D. V. Valovik

Penza State University, Penza

Abstract: The electromagnetic problem of TМ-waves propagation in a layer with arbitrary nonlinearity is considered. It is shown that the boundary value problem for Maxwell equations is reduced to a nonlinear boundary eigenvalue problem for a system of ordinary nonlinear differential equation of the 2${}$ order. Dispersion equation for the eigenvalues of the problem (propagation's constants) is obtained.

Keywords: Maxwell equation, diffraction problem, nonlinear boundary eigenvalue problem.

UDC: 517.958; 517.927.4