Smirnov, Y.; Schürmann, H. W.; Shestopalov, Y. Integral equation approach for the propagation of TE-waves in a nonlinear dielectric cylindrical waveguide. (English) Zbl 1067.35122 J. Nonlinear Math. Phys. 11, No. 2, 256-268 (2004). Summary: We consider the propagation of TE-polarized electromagnetic waves in cylindrical dielectric waveguides of circular cross section filled with lossless, nonmagnetic, and isotropic medium exhibiting a local Kerr-type dielectric nonlinearity. We look for axially-symmetric solutions and reduce the problem to the analysis of the associated cubic-nonlinear equation. We show that the solution in the form of a TE-polarized electromagnetic wave exists and can be obtained by iterating a cubic-nonlinear integral equation. We derive the associated dispersion equation and prove that it has a root that determines this solution. Cited in 17 Documents MSC: 35Q60 PDEs in connection with optics and electromagnetic theory 78A40 Waves and radiation in optics and electromagnetic theory Keywords:Maxwell equations; nonlinear second-order ordinary differential equation; nonlinear integral equation PDFBibTeX XMLCite \textit{Y. Smirnov} et al., J. Nonlinear Math. Phys. 11, No. 2, 256--268 (2004; Zbl 1067.35122) Full Text: DOI References: [1] Borgnis , F and Papas , C . 1958 .Electromagnetic Waveguides, in Handbuch der Physik, Edited by: Flügge , S . Vol. 16 , 24 Berlin : Springer Verlag . [2] Stratton J A, Electromagnetic Theory (1941) [3] Chiao R Y, Phys. Rev. Lett. 13 pp 479– (1964) [4] Eleonski V M, Sov. Phys. JETP 35 pp 44– (1972) [5] Chen Y, J. Opt. Soc. Am. B 8 pp 2338– (1991) [6] Akhmediev N N, Phys.Rev. A 46 pp 430– (1992) [7] Sammut R A, J. Opt. Soc. Am. B 8 pp 395– (1990) [8] Sjöberg D, Radio Science 38 pp 395– (2003) [9] Snyder A, Optical Waveguide Theory (1983) [10] Stakgold I, Green’s Functions and Boundary Value Problems (1998) [11] Trenogin V A, Functional Analysis (1993) [12] Zeidler E, Applied Functional Analysis (1997) [13] Akhmediev N N, The problem of Stability and Exitation of Nonlinear Surface Waves, in Modern Problems of Condensed Matter Sciences (1991) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.