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The paper focuses on the problem of monochromatic electromagnetic TM wave propagation in a two-layer circular cylindrical dielectric waveguide. The space outside thewaveguide is filled with isotropic medium having constant permittivity. The inner core ofthe waveguide is filled with isotropic medium having constant permittivity; the claddingof the core is filled with isotropic inhomogeneous nonlinear permittivity (the nonlinearterm is expressed by Kerr law). Existence of guided modes which depend harmonicallyon z (the waveguide axis coincides with z-axis) is proved and their localization is found. Numerical results including different type of nonlinearities are presented. A comparisonwith the linear case is given. The existence of a new propagation regime is predicted.

Guided Electromagnetic Waves Propagating in a Two-Layer Cylindrical Dielectric Waveguide with Inhomogeneous Nonlinear Permittivity