## Nonlinear transmission eigenvalue problem describing TE wave propagation in two-layered cylindrical dielectric waveguides.(Russian, English)Zbl 1299.78015

Zh. Vychisl. Mat. Mat. Fiz. 53, No. 7, 1150-1161 (2013); translation in Comput. Math. Math. Phys. 53, No. 7, 973-983 (2013).
Summary: The paper is concerned with propagation of surface TE waves in a circular nonhomogeneous two-layered dielectric waveguide filled with a Kerr nonlinear medium. The problem is reduced to the analysis of a nonlinear integral equation with a kernel in the form of a Green’s function. The existence of propagating TE waves is proved using the contraction mapping method. For the numerical solution of the problem, two methods are proposed: an iterative algorithm (whose convergence is proved) and a method based on solving an auxiliary Cauchy problem (the shooting method). The existence of roots of the dispersion equation (propagation constants of the waveguide) is proved. Conditions under which $$k$$ waves can propagate are obtained, and regions of localization of the corresponding propagation constants are found.

### MSC:

 78A50 Antennas, waveguides in optics and electromagnetic theory 45G05 Singular nonlinear integral equations
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### References:

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