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Gaps in the Spectrum of Thin Waveguides with Periodically Locally Deformed Walls

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Abstract

The structures of quantum and acoustic waveguides obtained by joining a periodic family of small knots to a thin cylinder are examined. Asymptotic expansions of eigenvalues of a model problem in the periodicity cell are obtained, which are used to derive asymptotic formulas for the disposition and sizes of the gaps in the spectra of the corresponding Dirichlet and Neumann problems for the Laplace operator. Geometric and integral characteristics of the waveguides are found that ensure the opening of several spectral gaps.

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Funding

This work was supported by the Russian Science Foundation, project no. 22-11-00046.

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  1. Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, 199178, St. Petersburg, Russia

    S. A. Nazarov

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  1. S. A. Nazarov
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Correspondence to S. A. Nazarov.

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Nazarov, S.A. Gaps in the Spectrum of Thin Waveguides with Periodically Locally Deformed Walls. Comput. Math. and Math. Phys. 64, 99–117 (2024). https://doi.org/10.1134/S0965542524010111

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  • DOI: https://doi.org/10.1134/S0965542524010111

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