On the solvability of a nonlinear eigenvalue boundary value problem for propagating TM waves in a circular nonlinear waveguide

Problem of propagation of TM-polarized electromagnetic waves in nonlinear dielectric waveguide with circular cross-section is considered. Waveguide filled nonlinear media with Kerr law. The problem is reduced to the nonlinear eigenvalue problem for integral operator-function. Contraction type principle is used for solving the problem. Numerical results are presented.