Geodesic
Linearizable and nonlinearizable solutions in the nonlinear eigenvalue problem arising in the theory of electrodynamic waveguides filled with a nonlinear medium
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018», November 23-28, 2018, Kazan. Part 2, Tome 176 (2020), pp. 34-49

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In this paper, we consider a nonlinear eigenvalue problem on a segment, which describes the propagation of monochromatic (polarized) electromagnetic TM waves in a planar dielectric waveguide filled with a nonlinear medium. Results on the solvability of the problem and properties of the eigenvalues are obtained.
Keywords: Maxwell's equations, nonlinear eigenvalue problem, asymptotics of eigenvalues, planar dielectric waveguide, nonlinear permittivity. 
@article{INTO_2020_176_a3,
     author = {D. V. Valovik and S. V. Tikhov},
     title = {Linearizable and nonlinearizable solutions in the nonlinear eigenvalue problem arising in the theory of electrodynamic waveguides filled with a nonlinear medium},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {34--49},
     publisher = {mathdoc},
     volume = {176},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_176_a3/}
}
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D. V. Valovik; S. V. Tikhov. Linearizable and nonlinearizable solutions in the nonlinear eigenvalue problem arising in the theory of electrodynamic waveguides filled with a nonlinear medium. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018», November 23-28, 2018, Kazan. Part 2, Tome 176 (2020), pp. 34-49. http://geodesic.mathdoc.fr/item/INTO_2020_176_a3/