Floquet theory for partial differential equations
P. A. Kuchment

This publication is cited in the following articles:

1. Xiang Ji, Xiaosen Yang, “Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems”, J. Phys.: Condens. Matter, 36:24 (2024), 243001  
2. P.-Y. Song, J.-F. Wei, Peng Xu, L.-L. Yan, M. Feng, Shi-Lei Su, Gang Chen, “Fast realization of high-fidelity nonadiabatic holonomic quantum gates with a time-optimal-control technique in Rydberg atoms”, Phys. Rev. A, 109:2 (2024)  
3. Andrey V. Shanin, Raphaël C. Assier, Andrey I. Korolkov, Oleg I. Makarov, “Double Floquet-Bloch transforms and the far-field asymptotics of Green's functions tailored to periodic structures”, Phys. Rev. B, 110:2 (2024)  
4. Matthew Faust, Wencai Liu, Rodrigo Matos, Jenna Plute, Jonah Robinson, Yichen Tao, Ethan Tran, Cindy Zhuang, “Floquet isospectrality of the zero potential for discrete periodic Schrödinger operators”, Journal of Mathematical Physics, 65:7 (2024)  
5. Justin T. Cole, Michael J. Nameika, “Data-driven approximations of topological insulator systems”, APL Machine Learning, 2:4 (2024)  
6. S. A. Nazarov, “Spectral gaps in a thin-walled infinite rectangular Dirichlet box with a periodic family of cross walls”, Sb. Math., 214:7 (2023), 982–1023              
7. Lucas Chesnel, Sergei A. Nazarov, “Spectrum of the Dirichlet Laplacian in a thin cubic lattice”, ESAIM: M2AN, 57:6 (2023), 3251  
8. Quan Yuan, Houjun Kang, Yaobing Zhao, Yunyue Cong, Xiaoyang Su, “Parametric resonance of multi-frequency excited MEMS based on homotopy analysis method”, Communications in Nonlinear Science and Numerical Simulation, 125 (2023), 107351  
9. Cheban D., “On the Structure of the Levinson Center For Monotone Non-Autonomous Dynamical Systems With a First Integral”, Carpathian J. Math., 38:1 (2022), 67–94    
10. Yuri A. Godin, Boris Vainberg, Mechanics and Physics of Structured Media, 2022, 191  
11. De Nittis G. Moscolari M. Richard S. Tiedra de Aldecoa R., “Spectral and Scattering Theory of One-Dimensional Coupled Photonic Crystals”, Rev. Math. Phys., 33:08 (2021), 2150027    
12. Kha M. Kuchment P., “Liouville-Riemann-Roch Theorems on Abelian Coverings Preface”: Kha, M Kuchment, P, Liouville-Riemann-Roch Theorems on Abelian Coverings, Lect. Notes Math., Lecture Notes in Mathematics, 2245, Springer International Publishing Ag, 2021, VII+  
13. Nazarov S.A., Chesnel L., “Transmission and Trapping of Waves in An Acoustic Waveguide With Perforated Cross-Walls”, Fluid Dyn., 56:8 (2021), 1070–1093    
14. St. Petersburg Math. J., 32:3 (2021), 531–550    
15. S. A. Nazarov, “Homogenization of Kirchhoff plates with oscillating edges and point supports”, Izv. Math., 84:4 (2020), 722–779                
16. S. A. Nazarov, “Threshold resonances and virtual levels in the spectrum of cylindrical and periodic waveguides”, Izv. Math., 84:6 (2020), 1105–1160                
17. Leugering G., Nazarov S.A., Taskinen J., “The Band-Gap Structure of the Spectrum in a Periodic Medium of Masonry Type”, Netw. Heterog. Media, 15:4 (2020)    
18. S. A. Nazarov, “Asymptotics of the Eigenvalues and Eigenfunctions of a Thin Square Dirichlet Lattice with a Curved Ligament”, Math. Notes, 105:4 (2019), 559–579            
19. M. V. Platonova, K. S. Ryadovkin, “Branching random walks on $\mathbf{Z}^d$ with periodic branching sources”, Theory Probab. Appl., 64:2 (2019), 229–248              
20. S. A. Nazarov, “Finite-dimensional approximations to the Poincaré–Steklov operator for general elliptic boundary value problems in domains with cylindrical and periodic exits to infinity”, Trans. Moscow Math. Soc., 80 (2019), 1–51      
21. S. A. Nazarov, “Waves in a Plane Rectangular Lattice of Thin Elastic Waveguides”, J Math Sci, 242:2 (2019), 227  
22. 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    
23. S. A. Nazarov, “The asymptotics of natural oscillations of a long two-dimensional Kirchhoff plate with variable cross-section”, Sb. Math., 209:9 (2018), 1287–1336                
24. S. A. Nazarov, “Breakdown of cycles and the possibility of opening spectral gaps in a square lattice of thin acoustic waveguides”, Izv. Math., 82:6 (2018), 1148–1195                
25. S. A. Nazarov, “Asymptotics of eigenvalues in spectral gaps of periodic waveguides with small singular perturbations”, J. Math. Sci. (N. Y.), 243:5 (2019), 746–773    
26. Fedor L. Bakharev, M. Eugenia Pérez, “Spectral gaps for the Dirichlet‐Laplacian in a 3‐D waveguide periodically perturbed by a family of concentrated masses”, Mathematische Nachrichten, 291:4 (2018), 556  
27. Piotr Kijanka, Wieslaw J. Staszewski, Pawel Packo, “Generalised semi-analytical method for excitability curves calculation and numerical modal amplitude analysis for Lamb waves”, Struct Control Health Monit, 25:7 (2018), e2172  
28. S. A. Nazarov, “Finite-Dimensional Approximations of the Steklov–Poincaré Operator for the Helmholtz Equation in Periodic Waveguides”, J Math Sci, 232:4 (2018), 461  
29. Marco Martins Afonso, Paolo Muratore-Ginanneschi, Sílvio M. A. Gama, Andrea Mazzino, “Eddy diffusivity of quasi-neutrally-buoyant inertial particles”, Phys. Rev. Fluids, 3:4 (2018)  
30. 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                
31. S. A. Nazarov, “The spectra of rectangular lattices of quantum waveguides”, Izv. Math., 81:1 (2017), 29–90                
32. 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          
33. 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          
34. Bakharev F.L., Taskinen J., “Bands in the Spectrum of a Periodic Elastic Waveguide”, Z. Angew. Math. Phys., 68:5 (2017), 102    
35. S. A. Nazarov, “Asymptotics of Eigenvalues in Spectral Gaps Under Regular Perturbations of Walls of a Periodic Waveguide”, J Math Sci, 226:4 (2017), 402  
36. A. Żak, M. Krawczuk, M. Palacz, Ł. Doliński, W. Waszkowiak, “High frequency dynamics of an isotropic Timoshenko periodic beam by the use of the Time-domain Spectral Finite Element Method”, Journal of Sound and Vibration, 409 (2017), 318  
37. F. L. Bakharev, G. Cardone, S. A. Nazarov, J. Taskinen, “Effects of Rayleigh Waves on the Essential Spectrum in Perturbed Doubly Periodic Elliptic Problems”, Integr. Equ. Oper. Theory, 88:3 (2017), 373  
38. E. I. Mogilevskii, “Instability of a liquid layer under periodic influence: Falling film in an alternating electric field”, Fluid Dyn, 52:2 (2017), 253  
39. 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          
40. Kuchment P., “An overview of periodic elliptic operators”, Bull. Amer. Math. Soc., 53:3 (2016), 343–414            
41. S. A. Nazarov, “Transmission Conditions in One-Dimensional Model of a Rectangular Lattice of Thin Quantum Waveguides”, J Math Sci, 219:6 (2016), 994  
42. S.A.. Nazarov, Jari Taskinen, “Spectral gaps for periodic piezoelectric waveguides”, Z. Angew. Math. Phys, 2015  
43. 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              
44. S. A. Nazarov, “Eigenmodes of a thin elastic layer between periodic rigid profiles”, Comput. Math. Math. Phys., 55:10 (2015), 1684–1697              
45. Cardone G., Nazarov S.A., Taskinen J., “Spectra of Open Waveguides in Periodic Media”, 269, no. 8, 2015, 2328–2364    
46. 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    
47. S. A. Nazarov, “Umov-Mandelshtam radiation conditions in elastic periodic waveguides”, Sb. Math., 205:7 (2014), 953–982                
48. 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                
49. 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                  
50. S. A. Nazarov, “Asymptotic behavior of spectral gaps in a regularly perturbed periodic waveguide”, Vestnik St.Petersb. Univ.Math, 46:2 (2013), 89  
51. S. A. Nazarov, “Gaps and eigenfrequencies in the spectrum of a periodic acoustic waveguide”, Acoust. Phys, 59:3 (2013), 272  
52. S. A. Nazarov, “The localization for eigenfunctions of the Dirichlet problem in thin polyhedra near the vertices”, Siberian Math. J., 54:3 (2013), 517–532        
53. B.G.ang Xia, D.H.ai Zhang, Jian Huang, Jin Meng, “QUASI-OPTICAL FREQUENCY SELECTIVE SURFACE FOR ATMOSPHERIC REMOTE SENSING APPLICATION”, PIER M, 32 (2013), 115  
54. 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  
55. S. A. Nazarov, K. Ruotsalainen, J. Taskinen, “Gaps in the spectrum of the Neumann problem on a perforated plane”, Dokl. Math, 86:1 (2012), 574  
56. 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  
57. S. A. Nazarov, “Asymptotics of eigenfrequencies in the spectral gaps caused by a perturbation of a periodic waveguide”, Dokl. Math, 86:3 (2012), 871  
58. Nazarov S.A., Ruotsalainen K., Taskinen Ya., “Lakuny v spektre zadachi neimana na perforirovannoi ploskosti”, Doklady Akademii nauk, 445:2 (2012), 151–151  
59. Nazarov S.A., “Asimptotika sobstvennykh chastot, poyavlyayuschikhsya vnutri lakun pri vozmuschenii periodicheskogo volnovoda”, Doklady akademii nauk, 447:4 (2012), 382–382  
60. S. A. Nazarov, “Discrete spectrum of cranked, branchy, and periodic waveguides”, St. Petersburg Math. J., 23:2 (2012), 351–379              
61. S. A. Nazarov, “On the spectrum of the Laplace operator on the infinite Dirichlet ladder”, St. Petersburg Math. J., 23:6 (2012), 1023–1045            
62. Nazarov S.A., “Lokalizovannye poverkhnostnye volny v periodicheskom sloe tyazheloi zhidkosti”, Prikladnaya matematika i mekhanika, 75:2 (2011), 338–351  
63. Nazarov, SA, “Essential spectrum of a periodic elastic waveguide may contain arbitrarily many gaps”, Applicable Analysis, 89:1 (2010), 109          
64. S. A. Nazarov, “An example of multiple gaps in the spectrum of a periodic waveguide”, Sb. Math., 201:4 (2010), 569–594                  
65. 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          
66. S. A. Nazarov, “Opening of a Gap in the Continuous Spectrum of a Periodically Perturbed Waveguide”, Math. Notes, 87:5 (2010), 738–756            
67. Nazarov S.A., “Gap in the essential spectrum of an elliptic formally self-adjoint system of differential equations”, Differential Equations, 46:5 (2010), 730–741      
68. S. A. Nazarov, “Formation of gaps in the spectrum of the problem of waves on the surface of a periodic channel”, Comput. Math. Math. Phys., 50:6 (2010), 1038–1054            
69. 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          
70. S. A. Nazarov, “A Gap in the Essential Spectrum of the Neumann Problem for an Elliptic System in a Periodic Domain”, Funct. Anal. Appl., 43:3 (2009), 239–241              
71. Cardone, G, “Gaps in the essential spectrum of periodic elastic waveguides”, Zamm-Zeitschrift fur Angewandte Mathematik und Mechanik, 89:9 (2009), 729          
72. Nazarov, SA, “Gaps in the essential spectrum of infinite periodic necklace-shaped elastic waveguide”, Comptes Rendus Mecanique, 337:3 (2009), 119        
73. 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              
74. Nazarov S.A., “Localized waves in a doubly periodic elastic plane with a periodic row of defects”, Dokl. Phys., 54:12 (2009), 540–545              
75. Peter Kuchment, “Tight frames of exponentially decaying Wannier functions”, J. Phys. A: Math. Theor, 42:2 (2009), 025203  
76. S. A. Nazarov, “Concentration of trapped modes in problems of the linearized theory of water waves”, Sb. Math., 199:12 (2008), 1783–1807                  
77. Nazarov, SA, “Rayleigh waves in an elastic half-layer with partly jammed periodic boundary”, Doklady Physics, 53:11 (2008), 600          
78. Manuel Barros, José L. Cabrerizo, Manuel Fernández, Alfonso Romero, “Magnetic vortex filament flows”, J Math Phys (N Y ), 48:8 (2007), 082904        
79. V. Goncharov, “Model of compactons on jet streams and their collapse”, Phys Rev E, 76:6 (2007), 066314        
80. Hatem Najar, “Lifshitz Tails for Acoustic Waves in Random Quantum Waveguide”, J Stat Phys, 128:4 (2007), 1093  
81. I. A. Taimanov, “Two-dimensional Dirac operator and the theory of surfaces”, Russian Math. Surveys, 61:1 (2006), 79–159                  
82. Springer Tracts in Modern Physics, 212, Electronic States in Crystals of Finite Size, 2006, 89  
83. 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          
84. Stability and Control: Theory, Methods and Applications, 20011088, Almost Periodic Solutions of Differential Equations in Banach Spaces, 2001, 235  
85. 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              
86. 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  
87. Peter Kuchment, Leonid A. Kunyansky, “Spectral Properties of High Contrast Band-Gap Materials and Operators on Graphs”, Experimental Mathematics, 8:1 (1999), 1  
88. I. A. Taimanov, “The Weierstrass Representation of Closed Surfaces in $\mathbb{R}^3$”, Funct. Anal. Appl., 32:4 (1998), 258–267              
89. I. A. Taimanov, “The global Weierstrass representation and its spectrum”, Russian Math. Surveys, 52:6 (1997), 1330–1332              
90. 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        
91. 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        
92. Alexander Figotin, Peter Kuchment, “Band-gap structure of the spectrum of periodic Maxwell operators”, J Statist Phys, 74:1-2 (1994), 447        
93. Fran�ois Alouges, Arnaud Debussche, “On the discretization of a partial differential equation in the neighborhood of a periodic orbit”, Numer. Math., 65:1 (1993), 143  
94. 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            
95. J.M. Li, S.J. Kiener, International Symposium on Antennas and Propagation Society, Merging Technologies for the 90's, 1990, 610  
96. I. M. Krichever, “Spectral theory of two-dimensional periodic operators and its applications”, Russian Math. Surveys, 44:2 (1989), 145–225            
97. 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          
98. V. S. Buslaev, “Semiclassical approximation for equations with periodic coefficients”, Russian Math. Surveys, 42:6 (1987), 97–125            
99. Alexis S Mahalov, “Mathematical investigation of periodic acoustical waveguides of an arbitrary shape”, Journal of Mathematical Analysis and Applications, 127:2 (1987), 569  
100. 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