Geodesic
The method of cauchy problem for solving a nonlinear eigenvalue transmission problem for TM waves propagating in a layer with arbitrary nonlinearity
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 1, pp. 74-89

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The problem of plane monochromatic TM waves propagating in a layer with an arbitrary nonlinearity is considered. The layer is placed between two semi-infinite media. Surface waves propagating along the material interface are sought. The physical problem is reduced to solving a nonlinear eigenvalue transmission problem for a system of two ordinary differential equations. A theorem on the existence and localization of at least one eigenvalue is proven. On the basis of this theorem, a method for finding approximate eigenvalues of the considered problem is proposed. Numerical results for Kerr and saturation nonlinearities are presented as examples. 
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     title = {The method of cauchy problem for solving a nonlinear eigenvalue transmission problem for {TM} waves propagating in a layer with arbitrary nonlinearity},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     language = {ru},
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D. V. Valovik; E. V. Zarembo. The method of cauchy problem for solving a nonlinear eigenvalue transmission problem for TM waves propagating in a layer with arbitrary nonlinearity. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 1, pp. 74-89. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_1_a7/