Nonlinearizable solutions in an eigenvalue problem for Maxwell's equations with nonhomogeneous nonlinear permittivity in a layer

DOI10.1111/SAPM.12512zbMath1529.34024MaRDI QIDQ6068090

Dmitry V. Valovik, Unnamed Author

Publication date: 15 December 2023

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

nonlinear eigenvalue problemMaxwell's equationnonlinear permittivitynonlinear guided waveeigenvalue asymptoticnonlinear plane waveguide

Mathematics Subject Classification ID

Antennas, waveguides in optics and electromagnetic theory (78A50) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20) Positive solutions to nonlinear boundary value problems for ordinary differential equations (34B18) Applications of boundary value problems involving ordinary differential equations (34B60) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15) Boundary eigenvalue problems for ordinary differential equations (34B09)

Related Items (1)

Maxwell's equations in a plane waveguide with nonhomogeneous nonlinear permittivity: analytical and numerical approaches

Cites Work

• On the existence of an infinite number of eigenvalues in one nonlinear problem of waveguide theory
• Maxwell's equations with arbitrary self-action nonlinearity in a waveguiding theory: guided modes and asymptotic of eigenvalues
• Perturbation method in the theory of propagation of two-frequency electromagnetic waves in a nonlinear waveguide. I: TE-TE waves
• Asymptotic analysis of a nonlinear eigenvalue problem arising in electromagnetics
• Asymptotical analysis of a nonlinear Sturm–Liouville problem: Linearisable and non-linearisable solutions
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