Trapped modes in angular joints of 2D waveguides

DOI10.1080/00036811.2013.786046zbMath1287.35049OpenAlexW2011871882MaRDI QIDQ5417858

Sergueï A. Nazarov, Andrey Shanin

Publication date: 22 May 2014

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036811.2013.786046

zbMATH Keywords

discrete spectrumtrapped modesbroken waveguides

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Scattering theory for PDEs (35P25) Eigenvalue problems for linear operators (47A75)

Related Items (17)

Existence of the discrete spectrum in the Fichera layers and crosses of arbitrary dimension ⋮ Spectrum of a problem of elasticity theory in the union of several infinite layers ⋮ Discrete spectrum of cranked quantum and elastic waveguides ⋮ The bound states of 3D Y-junction waveguides ⋮ Asymptotics of eigenvalues of the Dirichlet problem in a skewed ℐ-shaped waveguide ⋮ Spectra of three-dimensional cruciform and lattice quantum waveguides ⋮ Spectral gaps in a thin-walled infinite rectangular Dirichlet box with a periodic family of cross walls ⋮ Localization of eigenfunctions in the Dirichlet beaker ⋮ Embedded eigenvalues of the Neumann problem in a strip with a box-shaped perturbation ⋮ Discrete spectrum of cross-shaped quantum waveguides ⋮ Eigenvalue inequalities and absence of threshold resonances for waveguide junctions ⋮ Dirichlet spectrum of the Fichera layer ⋮ Bound states of waveguides with two right-angled bends ⋮ Waves in a plane rectangular lattice of thin elastic waveguides ⋮ Spectral asymptotics of the Dirichlet Laplacian in a conical layer ⋮ Criteria for the absence and existence of bounded solutions at the threshold frequency in a junction of quantum waveguides ⋮ Open waveguides in a thin Dirichlet ladder. I: Asymptotic structure of the spectrum

Cites Work

• Asymptotic formula for an eigenvalue of the Dirichlet problem in a cranked waveguide
• Plane waveguides with corners in the small angle limit
• CURVATURE-INDUCED BOUND STATES IN QUANTUM WAVEGUIDES IN TWO AND THREE DIMENSIONS
• Discrete spectrum of cranked, branching, and periodic waveguides
• Some recent results on the zeros of Bessel functions and orthogonal polynomials

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