Nonlinear TE-polarized electromagnetic waves in a cylindrical waveguide

In this work, we study TE-polarized electromagnetic waves propagating in an inhomogeneous dielectric waveguide of circular cross section filled with a medium; the nonlinearity is simulated by Kerr's law. For the numerical solution of the problem, an iterative algorithm is proposed, and its convergence is proved. The existence of the roots of the dispersion equation, the propagation constants of the waveguide, is proved. The conditions are obtained when several waves can propagate, the localization regions of the corresponding propagation constants are determined.