Geodesic
Propagation of TM waves in a layer with arbitrary nonlinearity
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 9, pp. 1729-1739 Cet article a éte moissonné depuis la source Math-Net.Ru

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A boundary value problem for Maxwell’s equations describing propagation of TM waves in a nonlinear dielectric layer with arbitrary nonlinearity is considered. The layer is located between two linear semi-infinite media. The problem is reduced to a nonlinear boundary eigenvalue problem for a system of second-order nonlinear ordinary differential equations. A dispersion equation for the eigenvalues of the problem (propagation constants) is derived. For a given nonlinearity function, the dispersion equation can be studied both analytically and numerically. A sufficient condition for the existence of at least one eigenvalue is formulated. 
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D. V. Valovik. Propagation of TM waves in a layer with arbitrary nonlinearity. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 9, pp. 1729-1739. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_9_a13/

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