Analytical solution for certain nonlinear electromagnetic field problems

The paper presents a nonlinear electromagnetic field problem with cylindrical symmetry. A time-sinusoidal boundary condition is applied, which yields non-sinusoidal steady-state fields. The problem is brought forth to test an analytical-numerical method based on the method of small parameter. A distinctive feature of this method is that it requires symbolic calculations to be performed. These allow to reduce the problem to a system of nonlinear equations. In order to check the accuracy of the solution, several error criteria are introduced. Moreover, the power balance of a nonlinear conductive region is verified.