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Uspekhi Mat. Nauk, 1982, Volume 37, Issue 4(226), Pages 3–52 (Mi umn3768)  

This article is cited in 65 scientific papers (total in 65 papers)

Floquet theory for partial differential equations

P. A. Kuchment

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English version:
Russian Mathematical Surveys, 1982, 37:4, 1–60

Bibliographic databases:

UDC: 517.9
MSC: 35J25, 35K20, 35L20, 35K90, 35S15
Received: 17.06.1981

Citation: P. A. Kuchment, “Floquet theory for partial differential equations”, Uspekhi Mat. Nauk, 37:4(226) (1982), 3–52; Russian Math. Surveys, 37:4 (1982), 1–60

Citation in format AMSBIB
\by P.~A.~Kuchment
\paper Floquet theory for partial differential equations
\jour Uspekhi Mat. Nauk
\yr 1982
\vol 37
\issue 4(226)
\pages 3--52
\jour Russian Math. Surveys
\yr 1982
\vol 37
\issue 4
\pages 1--60

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    This publication is cited in the following articles:
    1. P. A. Kuchment, “Spherical representation of solutions of invariant differential equations on a Riemannian symmetric space of noncompact type”, Math. USSR-Izv., 27:3 (1986), 535–548  mathnet  crossref  mathscinet  zmath
    2. V. S. Buslaev, “Semiclassical approximation for equations with periodic coefficients”, Russian Math. Surveys, 42:6 (1987), 97–125  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. Alexis S Mahalov, “Mathematical investigation of periodic acoustical waveguides of an arbitrary shape”, Journal of Mathematical Analysis and Applications, 127:2 (1987), 569  crossref
    4. P. G. Grinevich, S. P. Novikov, “Two-dimensional “inverse scattering problem” for negative energies and generalized-analytic functions. I. Energies below the ground state”, Funct. Anal. Appl., 22:1 (1988), 19–27  mathnet  crossref  mathscinet  zmath  isi
    5. I. M. Krichever, “Spectral theory of two-dimensional periodic operators and its applications”, Russian Math. Surveys, 44:2 (1989), 145–225  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. S. A. Nazarov, “Asymptotics of the solution of the Dirichlet problem for an equation with rapidly oscillating coefficients in a rectangle”, Math. USSR-Sb., 73:1 (1992), 79–110  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. Alexander Figotin, Peter Kuchment, “Band-gap structure of the spectrum of periodic Maxwell operators”, J Statist Phys, 74:1-2 (1994), 447  crossref  mathscinet  zmath  isi
    8. A. Figotin, P. Kuchment, “Band-Gap Structure of Spectra of Periodic Dielectric and Acoustic Media. II. Two-Dimensional Photonic Crystals”, SIAM J Appl Math, 56:6 (1996), 1561  crossref  mathscinet  zmath  isi
    9. Alex Figotin, Peter Kuchment, “Band-Gap Structure of Spectra of Periodic Dielectric and Acoustic Media. I. Scalar Model”, SIAM J Appl Math, 56:1 (1996), 68  crossref  mathscinet  zmath  isi
    10. I. A. Taimanov, “The global Weierstrass representation and its spectrum”, Russian Math. Surveys, 52:6 (1997), 1330–1332  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    11. I. A. Taimanov, “The Weierstrass Representation of Closed Surfaces in $\mathbb{R}^3$”, Funct. Anal. Appl., 32:4 (1998), 258–267  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    12. S. A. Nazarov, “The polynomial property of self-adjoint elliptic boundary-value problems and an algebraic description of their attributes”, Russian Math. Surveys, 54:5 (1999), 947–1014  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    13. Waldemar Axmann, Peter Kuchment, “An Efficient Finite Element Method for Computing Spectra of Photonic and Acoustic Band-Gap Materials”, Journal of Computational Physics, 150:2 (1999), 468  crossref
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    15. S. A. Nazarov, A. S. Slutskij, “Averaging of an elliptic system under condensing perforation of a domain”, St. Petersburg Math. J., 17:6 (2006), 989–1014  mathnet  crossref  mathscinet  zmath  elib
    16. I. A. Taimanov, “Two-dimensional Dirac operator and the theory of surfaces”, Russian Math. Surveys, 61:1 (2006), 79–159  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    17. Manuel Barros, José L. Cabrerizo, Manuel Fernández, Alfonso Romero, “Magnetic vortex filament flows”, J Math Phys (N Y ), 48:8 (2007), 082904  crossref  mathscinet  zmath  isi
    18. V. Goncharov, “Model of compactons on jet streams and their collapse”, Phys Rev E, 76:6 (2007), 066314  crossref  mathscinet  adsnasa  isi
    19. 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
    20. Nazarov, SA, “Rayleigh waves in an elastic half-layer with partly jammed periodic boundary”, Doklady Physics, 53:11 (2008), 600  crossref  zmath  adsnasa  isi  elib
    21. S. A. Nazarov, “Opening a gap in the essential spectrum of the elasticity problem in a periodic semi-layer”, St. Petersburg Math. J., 21:2 (2010), 281–307  mathnet  crossref  mathscinet  zmath  isi
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    23. Cardone, G, “Gaps in the essential spectrum of periodic elastic waveguides”, Zamm-Zeitschrift fur Angewandte Mathematik und Mechanik, 89:9 (2009), 729  crossref  mathscinet  zmath  isi  elib
    24. Nazarov, SA, “Gaps in the essential spectrum of infinite periodic necklace-shaped elastic waveguide”, Comptes Rendus Mecanique, 337:3 (2009), 119  crossref  adsnasa  isi  elib
    25. S. A. Nazarov, “Gap detection in the spectrum of an elastic periodic waveguide with a free surface”, Comput. Math. Math. Phys., 49:2 (2009), 323–333  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    26. Nazarov S.A., “Localized waves in a doubly periodic elastic plane with a periodic row of defects”, Dokl. Phys., 54:12 (2009), 540–545  mathnet  crossref  mathscinet  zmath  isi  elib  elib
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    30. 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  adsnasa  isi  elib
    31. S. A. Nazarov, “Opening of a Gap in the Continuous Spectrum of a Periodically Perturbed Waveguide”, Math. Notes, 87:5 (2010), 738–756  mathnet  crossref  crossref  mathscinet  isi  elib
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    36. Nazarov S.A., “Lokalizovannye poverkhnostnye volny v periodicheskom sloe tyazheloi zhidkosti”, Prikladnaya matematika i mekhanika, 75:2 (2011), 338–351  elib
    37. S. A. Nazarov, K. Ruotsalainen, J. Taskinen, “Spectral gaps in the Dirichlet and Neumann problems on the plane perforated by a doubleperiodic family of circular holes”, J Math Sci, 2012  crossref
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    39. S. A. Nazarov, “The asymptotic analysis of gaps in the spectrum of a waveguide perturbed with a periodic family of small voids”, J Math Sci, 2012  crossref
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    41. Nazarov S.A., Ruotsalainen K., Taskinen Ya., “Lakuny v spektre zadachi neimana na perforirovannoi ploskosti”, Doklady Akademii nauk, 445:2 (2012), 151–151  elib
    42. Nazarov S.A., “Asimptotika sobstvennykh chastot, poyavlyayuschikhsya vnutri lakun pri vozmuschenii periodicheskogo volnovoda”, Doklady akademii nauk, 447:4 (2012), 382–382  elib
    43. S. A. Nazarov, “Spectral properties of a thin layer with a doubly periodic family of thinning regions”, Theoret. and Math. Phys., 174:3 (2013), 343–359  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    44. S. A. Nazarov, “Asymptotic behavior of spectral gaps in a regularly perturbed periodic waveguide”, Vestnik St.Petersb. Univ.Math, 46:2 (2013), 89  crossref
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    48. S. A. Nazarov, “Gap opening around a given point of the spectrum of a cylindrical waveguide by means of gentle periodic perturbation of walls”, J. Math. Sci. (N. Y.), 206:3 (2015), 288–314  mathnet  crossref
    49. S. A. Nazarov, “Umov-Mandelshtam radiation conditions in elastic periodic waveguides”, Sb. Math., 205:7 (2014), 953–982  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    50. S. A. Nazarov, “Bounded solutions in a $\mathrm{T}$-shaped waveguide and the spectral properties of the Dirichlet ladder”, Comput. Math. Math. Phys., 54:8 (2014), 1261–1279  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    51. S.A.. Nazarov, Jari Taskinen, “Spectral gaps for periodic piezoelectric waveguides”, Z. Angew. Math. Phys, 2015  crossref
    52. F. L. Bakharev, S. A. Nazarov, “Gaps in the spectrum of a waveguide composed of domains with different limiting dimensions”, Siberian Math. J., 56:4 (2015), 575–592  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    53. S. A. Nazarov, “Eigenmodes of a thin elastic layer between periodic rigid profiles”, Comput. Math. Math. Phys., 55:10 (2015), 1684–1697  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    54. Cardone G., Nazarov S.A., Taskinen J., “Spectra of Open Waveguides in Periodic Media”, 269, no. 8, 2015, 2328–2364  crossref  isi
    55. 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
    56. Kuchment P., “An overview of periodic elliptic operators”, Bull. Amer. Math. Soc., 53:3 (2016), 343–414  crossref  mathscinet  zmath  isi  elib  scopus
    57. S. A. Nazarov, “The asymptotic behaviour of the scattering matrix in a neighbourhood of the endpoints of a spectral gap”, Sb. Math., 208:1 (2017), 103–156  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    58. S. A. Nazarov, “The spectra of rectangular lattices of quantum waveguides”, Izv. Math., 81:1 (2017), 29–90  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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    60. 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
    61. Bakharev F.L., Taskinen J., “Bands in the Spectrum of a Periodic Elastic Waveguide”, Z. Angew. Math. Phys., 68:5 (2017), 102  crossref  isi
    62. Gomez D. Nazarov S.A. Perez M.E., “Homogenization of Winkler-Steklov Spectral Conditions in Three-Dimensional Linear Elasticity”, Z. Angew. Math. Phys., 69:2 (2018), 35  crossref  isi
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