# Resonant Scattering and Generation of WavesThe Equivalent System of Nonlinear Integral Equations

Resonant Scattering and Generation of Waves: The Equivalent System of Nonlinear Integral Equations [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).] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# Resonant Scattering and Generation of WavesThe Equivalent System of Nonlinear Integral Equations

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# References (10)

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

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