Hybrid TE-TE-wave propagation in closed plane waveguide filled with nonlinear medium

Background. Analysis of new modes of wave propagation in planar nonlinear waveguide structures constitutes an important class of electromagnetic problems and leads to the emergence of new problem statements. The purpose of this work is to prove the existence of a solution of hybrid TE-TE wave propagation problem in a closed plane nonlinear waveguide. Material and methods. The proof of the existence of solutions to the main problem is based on the perturbation method, and the auxiliary problem is studied by the method of the integral characteristic equations. Results. In this research a condition for the existence of a solution to the auxiliary problem is found, and the solvability of the main problem in the vicinity of this solution is proved. Conclusions. The results obtained in this work are of interest for studying new modes of wave propagation in nonlinear media.