On a numerical method for solving a nonlinear boundary value eigenvalue problem for electromagnetic TM waves propagating in a layer with Kerr nonlinearity

The article considers electromagnetic TM-waves propagation in a layer with Kerr nonlinearity. The physical problem is reduced to a nonlinear boundary Eigenvalue problem for a system of two ordinary differential equations. A new method for solving the nonlinear boundary eigenvalue problem is suggested. The method can be applied to study more complicated nonlinearities. Some numerical results are shown.