Integral dispersion equation method in the problem on nonlinear waves in a circular waveguide. (English. Russian original) Zbl 1479.78022

Differ. Equ. 57, No. 10, 1333-1340 (2021); translation from Differ. Uravn. 57, No. 10, 1359-1366 (2021).
Summary: We study TE-polarized electromagnetic waves propagating in an inhomogeneous dielectric waveguide of circular cross-section filled with a nonlinear medium where the nonlinearity is described by Kerr’s law. The existence of infinitely many nonlinear waves (surface as well as leaky) is proved. Sufficient conditions under which several waves can propagate are found, and the localization domains of the corresponding propagation constants are determined.


78A60 Lasers, masers, optical bistability, nonlinear optics
78A50 Antennas, waveguides in optics and electromagnetic theory
78A40 Waves and radiation in optics and electromagnetic theory
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
35Q61 Maxwell equations
Full Text: DOI


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