Hybrid waves of a shielded waveguide with nonlinear inhomogeneous filling

Background. One of the main directions in an electrodynamics is the problem of waves propagate in a various waveguiding structures. Such tasks are widely used in practice. The purpose of the work is to prove the existence of a new nonlinear regimes of wave propagation.
Materials and methods. In the article modified shooting method is described.
Results. The existence of hybrid nonpolarized azimuthally symmetric waves that occurs only in the presence of nonlinearity is proved. Conclusion. The developed mathematical approach can be used to analyze wave propagation in more complicated nonlinear open waveguides.