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Zbl 1177.78050
Valovik, D.V.; Smirnov, Yu.G.
A nonlinear boundary eigenvalue problem for TM-polarized electromagnetic waves in a nonlinear layer. (English. Russian original)
[J] Russ. Math. 52, No. 10, 60-63 (2008); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2008, No. 10, 70-74 (2008). ISSN 1066-369X; ISSN 1934-810X/e

Summary: We consider the propagation of TM-polarized electromagnetic waves in a nonlinear dielectric layer located between two linear media. The nonlinearity in the layer is described by the Kerr law. We reduce the problem to a nonlinear boundary eigenvalue problem for a system of ordinary differential equations. We obtain a dispersion relation and a first approximation for eigenvalues of the problem. We compare the results with those obtained for the case of a linear medium in the layer.

MSC 2000:: *78A60 Lasers, etc.
78A40 Waves and radiation

Keywords: dispersion relation; boundary-value problem; Kerr nonlinearity

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Zentralblatt MATH Berlin [Germany]