Nonlinearizable guided electromagnetic waves in a waveguide filled with nonlinear media

The article deals with a problem of propagation of an electromagnetic two-frequency wave in an anisotropic plane nonlinear waveguide. The permittivity in the waveguide is perturbed both in linear and nonlinear parts. The problem reduces to a nonlinear two-parameter eigenvalue problem for Maxwell’s equations. Existence of nonlinearizable solutions to the problem is proved. The proof is based on applying of a novel unstandard perturbation approach, where the unperturbed problem is also nonlinear having nonlinearizable solutions. The developed approach has a potential to be used in the theory of nonlinear oscillations and vibrations. Numerical results are presented.