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

DOI10.1007/S00332-023-09962-6zbMath1527.35404MaRDI QIDQ6074809

Unnamed Author, Dmitry V. Valovik

Publication date: 19 October 2023

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

zbMATH Keywords

nonlinear eigenvalue problemnonlinear Sturm-Liouville problemnonlinear permittivityeigenvalue asymptoticMaxwell's equation plane dielectric waveguidenonhomogeneous permittivity

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Sturm-Liouville theory (34B24) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Antennas, waveguides in optics and electromagnetic theory (78A50) Lasers, masers, optical bistability, nonlinear optics (78A60) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Waves and radiation in optics and electromagnetic theory (78A40) Maxwell equations (35Q61) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Cites Work

• Guided electromagnetic waves propagating in a two-layer cylindrical dielectric waveguide with inhomogeneous nonlinear permittivity
• On a nonlinear eigenvalue problem related to the theory of propagation of electromagnetic waves
• On the existence of infinitely many eigenvalues in a nonlinear Sturm-Liouville problem arising in the theory of waveguides
• On spectral properties of the Sturm-Liouville operator with power nonlinearity
• Dual variational methods in critical point theory and applications
• Asymptotical analysis of a nonlinear Sturm–Liouville problem: Linearisable and non-linearisable solutions
• Nonlinearizable solutions in an eigenvalue problem for Maxwell's equations with nonhomogeneous nonlinear permittivity in a layer
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