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Sbornik: Mathematics, 2006, Volume 197, Issue 4, Pages 475–504
DOI: https://doi.org/10.1070/SM2006v197n04ABEH003767
(Mi sm1545)
 

This article is cited in 52 scientific papers (total in 52 papers)

Discrete spectrum of an asymmetric pair of waveguides coupled through a window

D. I. Borisovab

a Bashkir State Pedagogical University
b Nuclear Physics Institute, Academy of Sciences of the Czech Republic
References:
Abstract: In this paper one analyses the discrete spectrum of an asymmetric pair of two-dimensional quantum waveguides with common boundary in which a window of finite size is made. The phenomenon of new eigenvalues arising at the boundary of the essential spectrum as the length of the window passes over critical values is considered. For the newly arising eigenvalues one constructs asymptotic expansions with respect to the small parameter equal to the difference between the window length and the closest critical value. The behaviour of the spectrum under an unrestricted growth of the length of the window is also under investigation; asymptotic expansions for eigenvalues with respect to the large parameter, the length of the window, are constructed.
Bibliography: 22 titles.
Received: 17.08.2004 and 24.11.2005
Russian version:
Matematicheskii Sbornik, 2006, Volume 197, Number 4, Pages 3–32
DOI: https://doi.org/10.4213/sm1545
Bibliographic databases:
UDC: 517.958
MSC: 47F05, 47N50, 35P20
Language: English
Original paper language: Russian
Citation: D. I. Borisov, “Discrete spectrum of an asymmetric pair of waveguides coupled through a window”, Mat. Sb., 197:4 (2006), 3–32; Sb. Math., 197:4 (2006), 475–504
Citation in format AMSBIB
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\paper Discrete spectrum of an asymmetric pair of waveguides coupled through a~window
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\pages 3--32
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Linking options:
  • https://www.mathnet.ru/eng/sm1545
  • https://doi.org/10.1070/SM2006v197n04ABEH003767
  • https://www.mathnet.ru/eng/sm/v197/i4/p3
  • This publication is cited in the following 52 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:697
    Russian version PDF:202
    English version PDF:18
    References:74
    First page:2
     
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