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Mat. Sb., 1999, Volume 190, Number 2, Pages 43–70 (Mi msb383)  

This article is cited in 23 scientific papers (total in 23 papers)

Wood's anomalies and surface waves in the problem of scattering by a periodic boundary. II

I. V. Kamotskiia, S. A. Nazarovb

a Saint-Petersburg State University
b Admiral Makarov State Maritime Academy

Abstract: The solution of the problem of diffraction of an acoustic plane wave by a periodic boundary for frequencies close to threshold values is studied. It is shown that if the periodic structure has some special geometry, then the transformations of the diffraction pattern (Wood's anomalies) are accompanied by the occurrence of surface waves. Substantiation of asymptotic formulae (in particular, the ones in [1]) is carried out on the basis of the techniques of equivalent weighted norms in Sobolev spaces.

DOI: https://doi.org/10.4213/sm383

Full text: PDF file (364 kB)
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English version:
Sbornik: Mathematics, 1999, 190:2, 205–231

Bibliographic databases:

UDC: 517.9
MSC: 76Q05, 35P25, 35C20
Received: 08.07.1997

Citation: I. V. Kamotskii, S. A. Nazarov, “Wood's anomalies and surface waves in the problem of scattering by a periodic boundary. II”, Mat. Sb., 190:2 (1999), 43–70; Sb. Math., 190:2 (1999), 205–231

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. Kamotski, IV, “Trapped modes, surface waves and Wood's anomalies for gently sloped periodic boundaries”, Comptes Rendus de l Academie Des Sciences Serie II Fascicule B-Mecanique Physique Astronomie, 328:5 (2000), 423  crossref  zmath  isi  elib  scopus  scopus  scopus
    2. Grikurov V.E., Heikkola E., Neittaanmaki P., Plamenevskii B.A., “Numerical detection of surface waves in diffraction gratings”, Day on Diffraction 2001, Proceedings, 2001, 97–106  crossref  isi  scopus  scopus  scopus
    3. Grikurov, VE, “A method of searching for surface waves in diffraction gratings”, Doklady Mathematics, 66:1 (2002), 136  zmath  isi  elib
    4. Grikurov V.E., Heikkola E., Neittaanmäki P., Plamenevskii B.A., “On computation of scattering matrices and on surface waves for diffraction gratings”, Numer. Math., 94:2 (2003), 269–288  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    5. V. Zernov, A.V. Pichugin, J. Kaplunov, “Eigenvalue of a semi-infinite elastic strip”, Proceedings Mathematical Physical and Engineering Sciences, 462:2068 (2006), 1255  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    6. S. A. Nazarov, “A Criterion for the Existence of Decaying Solutions in the Problem on a Resonator with a Cylindrical Waveguide”, Funct. Anal. Appl., 40:2 (2006), 97–107  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    7. S. A. Nazarov, “On the concentration of the point spectrum on the continuous one in problems of the linearized theory of water-waves”, J. Math. Sci. (N. Y.), 152:5 (2008), 674–689  mathnet  crossref  elib
    8. S. A. Nazarov, “Concentration of trapped modes in problems of the linearized theory of water waves”, Sb. Math., 199:12 (2008), 1783–1807  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    9. S. A. Nazarov, “Trapped modes in a cylindrical elastic waveguide with a damping gasket”, Comput. Math. Math. Phys., 48:5 (2008), 816–833  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    10. Nazarov S.A, “GAP IN A CONTINUOUS SPECTRUM OF AN ELASTIC WAVEGUIDE WITH A PARTLY CLAMPED SURFACE”, Journal of Applied Mechanics and Technical Physics, 51:1 (2010), 114–124  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus  scopus
    11. S. A. Nazarov, “On the asymptotics of an eigenvalue of a waveguide with thin shielding obstacle and Wood's anomalies”, J. Math. Sci. (N. Y.), 178:3 (2011), 292–312  mathnet  crossref
    12. Nazarov S.A., “Trapped modes in a T-shaped waveguide”, Acoustical Physics, 56:6 (2010), 1004–1015  crossref  adsnasa  isi
    13. S. A. Nazarov, “Asymptotic expansions of eigenvalues in the continuous spectrum of a regularly perturbed quantum waveguide”, Theoret. and Math. Phys., 167:2 (2011), 606–627  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    14. S. A. Nazarov, “Asymptotics of trapped modes and eigenvalues below the continuous spectrum of a waveguide with a thin shielding obstacle”, St. Petersburg Math. J., 23:3 (2012), 571–601  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    15. Nazarov S.A., “Trapped Waves in a Cranked Waveguide with Hard Walls”, Acoustical Physics, 57:6 (2011), 764–771  crossref  mathscinet  adsnasa  isi  elib  scopus  scopus  scopus
    16. Nazarov S.A., “Zakhvachennye volny v kolenchatom volnovode s zhestkimi stenkami”, Akusticheskii zhurnal, 57:6 (2011), 746–754  elib
    17. G. Cardone, S. A. Nazarov, K. Ruotsalainen, “Asymptotic behaviour of an eigenvalue in the continuous spectrum of a narrowed waveguide”, Sb. Math., 203:2 (2012), 153–182  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    18. Kamotski I.V., Maz'ya V.G., “On the Linear Water Wave Problem in the Presence of a Critically Submerged Body”, SIAM J. Math. Anal., 44:6 (2012), 4222–4249  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    19. S. A. Nazarov, “The Mandelstam Energy Radiation Conditions and the Umov–Poynting Vector in Elastic Waveguides”, J Math Sci, 2013  crossref  mathscinet  scopus  scopus  scopus
    20. B. A. Plamenevskii, A. S. Poretckii, O. V. Sarafanov, “Method for computing waveguide scattering matrices in vicinity of thresholds”, St. Petersburg Math. J., 26:1 (2015), 91–116  mathnet  crossref  mathscinet  isi  elib
    21. S. A. Nazarov, “Almost standing waves in a periodic waveguide with a resonator and near-threshold eigenvalues”, St. Petersburg Math. J., 28:3 (2017), 377–410  mathnet  crossref  mathscinet  isi  elib
    22. Cardone G. Durante T. Nazarov S.A., “Embedded Eigenvalues of the Neumann Problem in a Strip With a Box-Shaped Perturbation”, J. Math. Pures Appl., 112 (2018), 1–40  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    23. S. A. Nazarov, “Zakhvat volny v iskrivlennom tsilindricheskom akusticheskom volnovode s neizmennym secheniem”, Algebra i analiz, 31:5 (2019), 154–183  mathnet
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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