Stabilizing solutions at thresholds of the continuous spectrum and anomalous transmission of waves

DOI10.1002/zamm.201500016OpenAlexW2302461619MaRDI QIDQ6065060

Andrey Shanin, Unnamed Author, Sergueï A. Nazarov

Publication date: 11 December 2023

Published in: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/zamm.201500016

zbMATH Keywords

scattering matrixthreshold behaviorwaveguide modesscattering in waveguides

Mathematics Subject Classification ID

Spectral theory and eigenvalue problems for partial differential equations (35Pxx) Elliptic equations and elliptic systems (35Jxx) Qualitative properties of solutions to partial differential equations (35Bxx)

Related Items (8)

Transmission of waves through a small aperture in the cross-wall in an acoustic waveguide ⋮ Scattering matrix at small frequencies in a junction of cylindrical acoustic waveguides ⋮ Almost complete transmission of waves through perforated cross-walls in a waveguide with Dirichlet boundary condition ⋮ Various manifestations of wood anomalies in locally distorted quantum waveguides ⋮ Scattering of low-frequency elastic waves in an infinite Kirchhoff plate ⋮ Waveguide with double threshold resonance at a simple threshold ⋮ Anomalies of acoustic wave propagation in two semi-infinite cylinders connected by a flattened ligament ⋮ The preservation of threshold resonances and the splitting off of eigenvalues from the threshold of the continuous spectrum of quantum waveguides

Cites Work

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• Perturbation theory for linear operators.
• Scattering anomalies in a resonator above the thresholds of the continuous spectrum
• Properties of Spectra of Boundary Value Problems in Cylindrical and Quasicylindrical Domains
• Existence theorems for trapped modes
• Method for computing waveguide scattering matrices in the vicinity of thresholds

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