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Zh. Vychisl. Mat. Mat. Fiz., 2017, Volume 57, Number 2, Pages 237–254 (Mi zvmmf10518)  

This article is cited in 2 scientific papers (total in 2 papers)

Open waveguides in a thin Dirichlet lattice: II. Localized waves and radiation conditions

S. A. Nazarovabc

a Peter the Great St. Petersburg State Polytechnical University, St. Petersburg, Russia
b Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia
c St. Petersburg State University, St. Petersburg, Russia

Abstract: Wave processes localized near an angular open waveguide obtained by thickening two perpendicular semi-infinite rows of ligaments in a thin square lattice of quantum waveguides (Dirichlet problem for the Helmholtz equation) are investigated. Waves of two types are discovered: the first are observed near the lattice nodes and almost do not affect the ligaments, while the second, on the contrary, excite oscillations in the ligaments, whereas the nodes stay relatively at rest. Asymptotic representations of the wave fields are derived, and radiation conditions are imposed on the basis of the Umov-Mandelstam energy principle.

Key words: open waveguides, square lattice, Dirichlet problem for the Helmholtz equation, asymptotic representations of wave fields, Umov–Mandelstam principle.

Funding Agency Grant Number
Saint Petersburg State University 0.38.237.2014


DOI: https://doi.org/10.7868/S0044466917020132

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English version:
Computational Mathematics and Mathematical Physics, 2017, 57:2, 236–252

Bibliographic databases:

Document Type: Article
UDC: 519.634
Received: 24.10.2015

Citation: S. A. Nazarov, “Open waveguides in a thin Dirichlet lattice: II. Localized waves and radiation conditions”, Zh. Vychisl. Mat. Mat. Fiz., 57:2 (2017), 237–254; Comput. Math. Math. Phys., 57:2 (2017), 236–252

Citation in format AMSBIB
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\paper Open waveguides in a thin Dirichlet lattice: II. Localized waves and radiation conditions
\jour Zh. Vychisl. Mat. Mat. Fiz.
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\pages 237--254
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\crossref{https://doi.org/10.7868/S0044466917020132}
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\jour Comput. Math. Math. Phys.
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\vol 57
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\pages 236--252
\crossref{https://doi.org/10.1134/S0965542517020129}
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    This publication is cited in the following articles:
    1. Bakharev F.L., Cardone G., Nazarov S.A., Taskinen J., “Effects of Rayleigh Waves on the Essential Spectrum in Perturbed Doubly Periodic Elliptic Problems”, Integr. Equ. Oper. Theory, 88:3 (2017), 373–386  crossref  mathscinet  zmath  isi
    2. S. A. Nazarov, “Asimptotika sobstvennykh chisel i funktsii tonkoi kvadratnoi reshetki Dirikhle s iskrivlennoi peremychkoi”, Matem. zametki, 105:4 (2019), 564–588  mathnet  crossref  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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