Asymptotic Analysis of a Nonlinear Eigenvalue Problem Arising in the Waveguide Theory

Author:

Valovik D. V.,Tikhov S. V.

Publisher

Pleiades Publishing Ltd

Subject

General Mathematics,Analysis

Reference19 articles.

1. Gokhberg, I.Ts. and Krein, M.G., Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov (Introduction to the Theory of Linear Nonself-Adjoint Operators), Moscow: Nauka, 1965.

2. Eleonskii, P.N., Oganes’yants, L.G., and Silin, V.P., Cylindrical nonlinear waveguides, Sov. Phys. JETP, 1972, vol. 35, no. 1, pp. 44–47.

3. Vainshtein, L.A., Elektromagnitnye volny (Electromagnetic Waves), Moscow: AST, 1988.

4. Boardman, A.D., Egan, P., Lederer, F., Langbein, U., and Mihalache, D., Third-Order Nonlinear Electromagnetic TE and TM Guided Waves, Amsterdam London New York Tokyo: Elsevier Sci., 1991. (Reprinted from Nonlinear Surface Electromagnetic Phenomena, Ponath, H.-E. and Stegeman, G.I., Eds.)

5. Smirnov, Yu.G. and Valovik, D.V., On the infinitely many nonperturbative solutions in a transmission eigenvalue problem for Maxwell’s equations with cubic nonlinearity, J. Math. Phys., 2016, vol. 57, no. 10, p. 103504.

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