Eigenvalue problem that describes electromagnetic TE-wave propagation in a plane dielectric waveguide with nonlinear inhomogeneous media

Background. The aim of this work is to study the problem of electromagnetic TE- waves propagation in a plane nonlinear inhomogeneous dielectric waveguide. Materials and methods. The author used general methods of the theory of boundary value problems, the semi-conversion method (reduction of the differential equation to the integral equation using the Green's function), the contracting mapping method. Results. The researcher has obtained a dispersion equation and proved existence of dispersion equation's roots (propagation constants). The regions of localization of the propagation constants have been found. Numerical results (graphics of dispersion curves and eigenfunctions of the problem) have been presented. Conclusions. The obtained results can be used in the study of the problem of coupled electromagnetic waves propagation.