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Numerical Study of the Azimuthal Symmetric Hybrid Waves in a Nonlinear Cylindrical Waveguide

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Nonlinear and Inverse Problems in Electromagnetics (PIERS 2017, PIERS 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 243))

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Abstract

The propagation of monochromatic nonlinear symmetric hybrid waves in a cylindrical nonlinear dielectric waveguide is considered. The physical problem is reduced to solving a transmission eigenvalue problem for a system of ordinary differential equations. Spectral parameters of the problem are propagation constants of the waveguide. Numerical results are found with the modification of the shooting method. The method allows us to determine approximate eigenvalues with any prescribed accuracy. The comparison with known exact solutions (for particular values of parameters) are made. The approach described in this paper can be applied to other problems, e.g., to multilayered inhomogeneous waveguides.

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Acknowledgements

This study is supported by the Ministry of Education and Science of the Russian Federation, Project No. 1.894.2017/4.6.

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Authors and Affiliations

  1. Penza State University, 40 Krasnaya Street, Penza, 440026, Russia

    E. Smolkin

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  1. E. Smolkin
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Correspondence to E. Smolkin .

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Editors and Affiliations

  1. Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Gothenburg, Sweden

    L. Beilina

  2. Penza State University, Penza, Russia

    Yu. G. Smirnov

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Smolkin, E. (2018). Numerical Study of the Azimuthal Symmetric Hybrid Waves in a Nonlinear Cylindrical Waveguide. In: Beilina, L., Smirnov, Y. (eds) Nonlinear and Inverse Problems in Electromagnetics. PIERS PIERS 2017 2017. Springer Proceedings in Mathematics & Statistics, vol 243. Springer, Cham. https://doi.org/10.1007/978-3-319-94060-1_6

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