Geodesic
Nonlinear propagation of coupled electromagnetic waves in a circular cylindrical waveguide
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 8, pp. 1304-1320

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The problem of the propagation of coupled surface electromagnetic waves in a two-layer cylindrical circular waveguide filled with an inhomogeneous nonlinear medium is considered. A nonlinear coupled TE-TM wave is characterized by two (independent) frequencies $\omega_e$ and $\omega_m$ and two propagation constants $\widehat\gamma_e$ and $\widehat\gamma_m$. The physical problem reduces to a nonlinear two-parameter eigenvalue problem for a system of nonlinear ordinary differential equations. The existence of eigenvalues $(\widehat\gamma_e, \widehat\gamma_m)$ in proven and intervals of their localization are determined. 
@article{ZVMMF_2017_57_8_a6,
     author = {D. V. Valovik and E. Yu. Smol'kin},
     title = {Nonlinear propagation of coupled electromagnetic waves in a circular cylindrical waveguide},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1304--1320},
     publisher = {mathdoc},
     volume = {57},
     number = {8},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_8_a6/}
}
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D. V. Valovik; E. Yu. Smol'kin. Nonlinear propagation of coupled electromagnetic waves in a circular cylindrical waveguide. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 8, pp. 1304-1320. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_8_a6/