On the propagation of electromagnetic waves in cylindrical inhomogeneous dielectric waveguides filled with a nonlinear medium

The article investigates surface electromagnetic TE waves propagating along the axis of an inhomogeneous dielectric nonlinear cylindrical waveguide.. The nonlinearity inside the waveguide is described by Kerr law. Physical problem is reduced to a nonlinear integral equation. The kernel of the integral equation is the Green function for a linear differential operator. Existence of surface waves is proved with the help of the Schauder principle and the contraction method. For numerical solution of the problem an iteration method is suggested. Convergence of the numerical method is proved. It is also proved that the roots of the dispersion equation exist. These roots are propagation constants. Conditions when k propagating modes exist are found. Domains of localization of the propagation constants are given.