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The propagation of TE-polarized electromagnetic waves along a Kerr-type nonlinear dielectric, nonabsorbing, nonmagnetic, and isotropic (circular) cylindrical waveguide is investigated. For axially (azimuthal) symmetric solutions the problem is reduced to a cubic-nonlinear integral equation that is solved by iteration leading to a sequence uniformly convergent to the solution of the integral equation. The dispersion relations associated to the exact and iterate solutions, respectively, are derived and solved, subject to certain constraints. The roots of the exact dispersion relation are approximated by the roots of the dispersion relations generated by the iterate solutions. All statements of existence and convergence are based on results of a previous paper. Numerical results (concerning solutions of dispersion relations, field patterns, dependence of the propagation constant and of the cutoff radius on the nonlinearity parameter, power flow) are included.

We consider the propagation of TE-polarized electromagnetic waves in cylindrical dielectric waveguides of circular cross section filled with lossless, nonmagnetic, and isotropic medium exhibiting a local Kerr-type dielectric nonlinearity. We look for axially-symmetric solutions and reduce the problem to the analysis of the associated cubic-nonlinear equation. We show that the solution in the form of a TE-polarized electromagnetic wave exists and can be obtained by iterating a cubic-nonlinear integral equation. We derive the associated dispersion equation and prove that it has a root that determines this solution.