Nonlinear coupled wave propagation in a n-dimensional layer

Yury G. Smirnov and Dmitry V. Valovik

Applied Mathematics and Computation, 2017, vol. 294, issue C, 146-156

Abstract: The paper focuses on the generalization of a nonlinear multi-parameter eigenvalue problem for a system of nonlinear differential equations. The problem is reduced to a system of nonlinear integral equations on a segment. The notion of eigentuple is introduced, the existence of a finite number of isolated eigentuples is proved, and their distribution is described. The corresponding linear multi-parameter eigenvalue problem is studied as well; it is proved that the linear problem has an infinite number of isolated eigentuples. Applications to nonlinear electromagnetic wave propagation theory are demonstrated.

Keywords: Nonlinear multi-parameter eigenvalue problem; Linear multi-parameter eigenvalue problem; Eigentuples; Maxwell’s equations; Nonlinear guided wave; Dispersion equation (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:294:y:2017:i:c:p:146-156

DOI: 10.1016/j.amc.2016.09.011

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