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Algebra i Analiz, 2011, Volume 23, Issue 2, Pages 206–247 (Mi aa1239)  

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

Research Papers

Discrete spectrum of cranked, branchy, and periodic waveguides

S. A. Nazarov

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

Full text: PDF file (408 kB)
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English version:
St. Petersburg Mathematical Journal, 2012, 23:2, 351–379

Bibliographic databases:

Received: 10.10.2009

Citation: S. A. Nazarov, “Discrete spectrum of cranked, branchy, and periodic waveguides”, Algebra i Analiz, 23:2 (2011), 206–247; St. Petersburg Math. J., 23:2 (2012), 351–379

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. A. Nazarov, “On the spectrum of the Laplace operator on the infinite Dirichlet ladder”, St. Petersburg Math. J., 23:6 (2012), 1023–1045  mathnet  crossref  mathscinet  isi  elib  elib
    2. Nazarov S.A., “Trapped waves in a cranked waveguide with hard walls”, Acoustical Physics, 57:6 (2011), 764–771  crossref  mathscinet  adsnasa  isi  elib  elib  scopus
    3. Nazarov S.A., “Asimptotika sobstvennogo chisla zadachi dirikhle v kolenchatom volnovode”, Vestn. Sankt-Peterburgskogo un-ta. Ser. 1. Matem. Mekh. Astronom., 2011, no. 3, 29–35  zmath  elib
    4. Cardone G., Nazarov S.A., Ruotsalainen K., “Bound States of a Converging Quantum Waveguide”, ESAIM-Math. Model. Numer. Anal.-Model. Math. Anal. Numer., 47:1 (2013), 305–315  crossref  mathscinet  zmath  isi  scopus
    5. Nazarov S.A., “Asimptoticheskie svoistva spektra zadachi o volnakh v ogranichennom ob'eme dvukhsloinoi zhidkosti”, Prikladnaya matematika i mekhanika, 77:5 (2013), 690–710  elib
    6. Nazarov S.A., Ruotsalainen K., Uusitalo P., “The Y-Junction of Quantum Waveguides”, ZAMM-Z. Angew. Math. Mech., 94:6 (2014), 477–486  crossref  mathscinet  zmath  isi  elib  scopus
    7. Nazarov S.A., Shanin A.V., “Trapped Modes in Angular Joints of 2D Waveguides”, Appl. Anal., 93:3 (2014), 572–582  crossref  mathscinet  zmath  isi  elib  scopus
    8. Nazarov S.A., Ruotsalainen K., Uusitalo P., “Bound States of Waveguides With Two Right-Angled Bends”, J. Math. Phys., 56:2 (2015), 021505  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    9. Uusitalo P., “The Bound States of 3D Y-Junction Waveguides”, Ann. Acad. Sci. Fenn. Ser. A1-Math., 40:1 (2015), 329–341  crossref  mathscinet  zmath  isi  scopus
    10. Bakharev F.L., Matveenko S.G., Nazarov S.A., “Spectra of Three-Dimensional Cruciform and Lattice Quantum Waveguides”, Dokl. Math., 92:1 (2015), 514–518  crossref  mathscinet  zmath  isi  elib  scopus
    11. Wang C.Y., “Complex Trapped Modes of the Helmholtz Equation in Cross, S, and U Bends”, Int. J. Appl. Mech., 7:2 (2015), 1550024  crossref  isi  elib  scopus
    12. Exner P., Kovarik H., Quantum Waveguides, Theoretical and Mathematical Physics, Springer-Verlag Berlin, 2015, 1–382  crossref  mathscinet  isi
    13. S. A. Nazarov, “Discrete spectrum of cranked quantum and elastic waveguides”, Comput. Math. Math. Phys., 56:5 (2016), 864–880  mathnet  crossref  crossref  isi  elib
    14. Nazarov S.A., Ruotsalainen K., Uusitalo P., “Localized Waves in Carbon Nano-Structures With Connected and Disconnected Open Waveguides”, Mater. Phys. Mech., 29:2 (2016), 116–124  isi
    15. S. A. Nazarov, “Open waveguides in a thin Dirichlet ladder: I. Asymptotic structure of the spectrum”, Comput. Math. Math. Phys., 57:1 (2017), 156–174  mathnet  crossref  crossref  isi  elib
    16. S. A. Nazarov, “Open waveguides in a thin Dirichlet lattice: II. Localized waves and radiation conditions”, Comput. Math. Math. Phys., 57:2 (2017), 236–252  mathnet  crossref  crossref  isi  elib
    17. Pankrashkin K., “Eigenvalue inequalities and absence of threshold resonances for waveguide junctions”, J. Math. Anal. Appl., 449:1 (2017), 907–925  crossref  mathscinet  zmath  isi  scopus
    18. Bakharev F.L., Matveenko S.G., Nazarov S.A., “Examples of Plentiful Discrete Spectra in Infinite Spatial Cruciform Quantum Waveguides”, Z. Anal. ihre. Anwend., 36:3 (2017), 329–341  crossref  mathscinet  zmath  isi  scopus
    19. Amore P., Boyd J.P., Fernandez F.M., Jacobo M., Zhevandrov P., “Bound States in Weakly Deformed Waveguides: Numerical Versus Analytical Results”, Anziam J., 59:2 (2017), 200–214  crossref  mathscinet  zmath  isi  scopus
    20. Nazarov S.A., “Spectrum of a Problem of Elasticity Theory in the Union of Several Infinite Layers”, Russ. J. Math. Phys., 25:1 (2018), 73–87  crossref  mathscinet  zmath  isi  scopus
    21. 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
    22. Lifshits M., Nazarov A., “On Brownian Exit Times From Perturbed Multi-Strips”, Stat. Probab. Lett., 147 (2019), 1–5  crossref  mathscinet  zmath  isi  scopus
    23. 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
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