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References (10)
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P. Müller (1960)
W.D. Kupradse, Randwertaufgaben der Schwingungstheorie und Integralgleichungen (Hochschulbücher für Mathematik, Band 21). VIII + 239 S. m. 11 Abb. Berlin 1956. Deutscher Verlag der Wissenschaften. Preis geb. DM 27,60Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik, 40
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L. Angermann, V. Yatsyk (2011)
Resonance Properties of Scattering and Generation of Waves on Cubically Polarisable Dielectric Layers -
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L. Angermann, V. Yatsyk (2011)
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L. Angermann, Y. Shestopalov, V. Yatsyk (2013)
Mathematical models for scattering and generation of plane wave packets on layered cubically polarisable structuresFar east journal of applied mathematics, 81
- Publisher
- Springer International Publishing
- Copyright
- © Springer International Publishing AG, part of Springer Nature 2019
- ISBN
- 978-3-319-96300-6
- Pages
- 55 –76
- DOI
- 10.1007/978-3-319-96301-3_3
- Publisher site
- See Chapter on Publisher Site
Abstract
[In this chapter, we show how the problem (1.47), (C1)–(C4) can be reduced to finding solutions of a system of one-dimensional nonlinear integral equations w.r.t. the components un(z),\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u_n(z),$$\end{document}n=1,2,3,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=1,2,3,$$\end{document}z∈Icl,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z\in \mathscr {I}^\text {cl},$$\end{document} of the fields scattered and generated in the nonlinear layer. Here, we give a derivation of these equations, which is more formally than in the papers[1–7], and which extends the results of the works [8, 9] to the case of excitation of the nonlinear structure by the plane-wave packets (1.51).]
Published: Jul 27, 2018