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 Zap. Nauchn. Sem. POMI, 2014, Volume 422, Pages 90–130 (Mi znsl5765)

Gap opening around a given point of the spectrum of a cylindrical waveguide by means of gentle periodic perturbation of walls

S. A. Nazarovab

a St. Petersburg State University, St. Petersburg, Russia
b Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia

Abstract: We discuss one of the main questions in band-gap engineering, namely by an asymptotic analysis it is proven that any given point of a certain interval in the spectrum of a cylindrical waveguide can be surrounded with a spectral gap by means of a periodical perturbation of the walls. Both the Dirichlet and Neumann boundary conditions for the Laplace operator are considered in planar and multi-dimensional waveguides.

Key words and phrases: Dirichlet and Neumann spectral problems for Laplace operator, periodic wave guide, lacuna, uncoupling of spectral segments.

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English version:
Journal of Mathematical Sciences (New York), 2015, 206:3, 288–314

Document Type: Article
UDC: 517.956.8+517.958+539.3(2)

Citation: S. A. Nazarov, “Gap opening around a given point of the spectrum of a cylindrical waveguide by means of gentle periodic perturbation of walls”, Mathematical problems in the theory of wave propagation. Part 43, Zap. Nauchn. Sem. POMI, 422, POMI, St. Petersburg, 2014, 90–130; J. Math. Sci. (N. Y.), 206:3 (2015), 288–314

Citation in format AMSBIB
\Bibitem{Naz14} \by S.~A.~Nazarov \paper Gap opening around a~given point of the spectrum of a~cylindrical waveguide by means of gentle periodic perturbation of walls \inbook Mathematical problems in the theory of wave propagation. Part~43 \serial Zap. Nauchn. Sem. POMI \yr 2014 \vol 422 \pages 90--130 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl5765} \transl \jour J. Math. Sci. (N. Y.) \yr 2015 \vol 206 \issue 3 \pages 288--314 \crossref{https://doi.org/10.1007/s10958-015-2312-x} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84953359433}