The Cauchy problem method for solving the nonlinear eigenvalue conjugation problem for TM waves propagating in a circular two-layer dielectric waveguide with Kerr nonlinearity

The author investigates a problem of electromagnetic TM wave propagation in a two layered dielectric circle waveguide. One layer inside the waveguide is filled with Kerr medium. The physical problem is reduced to the nonlinear eigenvalue conjugation problem for a system of two ordinary differential equations. Theorem of eigenvalue existence is proved. The numerical method based on this theorem is suggested and its convergence is proved as well.