Monographs

  1. A. Comech, A. Komech, E. Kopylova, Attractors of Hamilton Nonlinear Partial Differential Equations. Chapter in: Partial Differential Equations and Functional Analysis, Birkhauser, 2023.

  2. A. Komech, E. Kopylova, Attractors of Hamilton Nonlinear Partial Differential Equations, Cambridge University Press, Cambridge, 2021.

  3. A. Komech, E. Kopylova, Dispersion Decay and Scattering Theory, John Wiley & Sons, Hoboken, NJ, 2012.

Papers

  1. E. Kopylova, Solitons type asymptotics for the Klein-Gordon equation coupled to nonlinear oscillator . Nonlinear Diff. Eqn. and Appl . 32 (2025), no.4.

  2. A. Komech, E. Kopylova, On momentum map for the Maxwell--Lorentz equations with spinning particle . International Journal of Geom. Methods in Modern Physics . 22 (2025), no. 9, 2550057.

  3. E. Kopylova, On asymptotic stability of solitons for 2D Maxwell--Lorentz equations with spinning particle . Monatshefte für Mathematik . 207 (2025), 59-82.

  4. E. Kopylova, A. Komech, Global attraction to solitons for 2D Maxwell--Lorentz equations with spinning particle . St. Petersburg Math. Journal . 35 (2024), 827-838.

  5. A. Komech, E. Kopylova, On orbital stability of solitons for 2D Maxwell--Lorentz equations . Pure Appl. Anal . 24 (2024), 325-338.

  6. E. Kopylova, A. Komech, On asymptotic stability of solitons for 2D Maxwell--Lorentz equations . Journal Math. Physics . 64 (2023), no. 10, 101504.

  7. A. Komech, E. Kopylova, On the Hamilton--Poisson structure and solitons for the Maxwell--Lorentz equations with spinning particle . J. Math. Anal. Appl . 522 (2023), no. 2, 126976.

  8. A. Komech, E. Kopylova, On the Stability of Solitons for the Maxwell-Lorentz Equations with Rotating Particle . Milan Journal of Mathematics . (2023).

  9. E. Kopylova, G. Teschl, Scattering properties and dispersion estimates for one dimensional discrete Dirac equation . Mathematische Nachrichten . 295 (2022), no. 44, 762-784.

  10. A. Komech, E. Kopylova, On global attractors for 2D damped driven nonlinear Schrödinger equations . Applicable Analysis . 101 (2022), no. 15, 5490-5503.

  11. E. Kopylova, Global attractor for 3D Dirac equation with nonlinear point interaction . Nonlinear Differential Equations and Applications NoDEA . 29 (2022), no. 3, 1-44.

  12. E. Kopylova, Klein-Gordon equation with mean field interaction. Orbital and asymptotic stability of solitary waves . Nonlinearity . 35 (2022), no. 7, 3593-3629.

  13. E. Kopylova, On dispersive estimates for one-dimensional Klein-Gordon equations . Asympt. Analysis . 127 (2022), 1-13.

  14. A. Comech, E. Kopylova, On spectral and orbital stability for the Klein-Gordon equation coupled to an anharmonic oscillator . Comm. Pure Appl. Anal . 20 (2021), no. 6, 2187-2209.

  15. A. Komech, E. Kopylova, Attractors of Hamilton nonlinear partial differential equations . Russian Math. Surveys . 75 (2020), no. 1, 1-87.

  16. E. Kopylova, A. Komech, Global attractor for 1D Dirac field coupled to nonlinear oscillator . Comm. Math. Physics . 375 (2020), no. 2, 573-603.

  17. E. Kopylova, A. Komech, On global attractor of 3D Klein-Gordon with several concentrated nonlinearities . Dynamics of PDEs . 16 (2019), no. 2, 105-124.

  18. A. Komech, E. Kopylova, On the dispersion decay for crystals in the linearized Schrödinger-Poisson model . J. Math. Anal. Appl . 50 (2018), no. 1, 864-882.

  19. E. Kopylova, On Dispersion decay for 3D Klein-Gordon equation . Discrete and Continuous Dynamical System . 38 (2018), no. 11, 5765-5780.

  20. A. Komech, E. Kopylova, On orbital stability of ground states for finite crystals in fermionic Schrödinger-Poisson model . SIAM J. Math. Anal . 50 (2018), no. 1, 64-85. ArXiv 1711.02938

  21. E. Kopylova, On global attraction to stationary states for wave equations with concentrated nonlinearities . J. Dynamics and Differential Equations . 30 (2018), no. 1, 107-116. ArXiv 1611.04463

  22. A. Komech, E. Kopylova, H. Spohn, On global attractors and radiation damping for nonrelativistic particle coupled to scalar field . St. Petersburg Math. J . 29 (2018), no. 2, 249-266. ArXiv 1611.03272

  23. E. Kopylova, On global attraction to solitary waves for the Klein -Gordon equation with concentrated nonlinearity . Nonlinearity . 30 (2017), 4191-4207. ArXiv 1611.09882

  24. A. Komech, E. Kopylova, On stability of ground states for finite crystals in the Schrödinger-Poisson model . J. Math. Phys . 58 (2017), no. 3, 031902. ArXiv 1511.07074

  25. E. Kopylova, On global well-posedness for Klein-Gordon equation with concentrated nonlinearity . J. Math. Anal. Appl. . 443 (2016), no. 2, 1142-1157. ArXiv 1607.00377

  26. A. Komech, E. Kopylova, On linear stability of crystals in the Schrödinger-Poisson model . J. Stat. Phys . 165 (2016), no. 2, 246-273. ArXiv 1505.07074

  27. A. Komech, E. Kopylova, Asymptotic stability of stationary states in wave equation coupled to nonrelativistic particle , Russ. J. Math. Phys. 23 (2016), no. 1, 93-100. ArXiv 1511.08680

  28. I. Egorova, E. Kopylova, V. Marchenko, G. Teschl, Dispersion Estimates for One-Dimensional Schrödinger and Klein-Gordon Equations Revisited , Russian Math. Surveys . 71 (2016), no. 3, 391-415. ArXiv 1411.0021

  29. E. Kopylova, G. Teschl, Dispersion estimates for one-dimensional discrete Dirac equations , J. Math. Anal. Appl. . 434 (2016), no. 1, 191-208. ArXiv 1507.02126

  30. I. Egorova, E. Kopylova, G. Teschl, Dispersion estimates for one-dimensional discrete Schrödinger and wave equations , Journal of Spectral Theory . 5 (2015), no. 4, 663-696. ArXiv 1403.7803

  31. E. Kopylova, Limiting absorption principle for the 1D discrete Dirac equation , Russ. J. Math. Phys. . 22 (2015), no. 1, 34-38.

  32. A. Komech, E. Kopylova, Weighted energy decay for magnetic Klein-Gordon equations , Applicable Analysis . 94 (2015), no. 2, 219-233.

  33. A. Komech, E. Kopylova, On the eigenfunction expansion for the Hamilton operators , Journal of Spectral Theory . 5 (2015), no. 2, 331-361. ArXiv 1405.4122

  34. A. Komech, E. Kopylova, On eigenfunction expansion of solutions to the Hamilton equations , Journal of Statistical Physics . 154 (2014), no. 1-2, 503-521. ArXiv 1308.0485

  35. E. Kopylova, On dispersion decay for discrete wave estimates for 2D Dirac equation , Comm. Math. Anal. , 17 (2014), no. 2, 209-216.

  36. E. Kopylova, Dispersion estimates for 2D Dirac equation , Asymptotic Analysis , 84 (2013), 35-46.

  37. E. Kopylova, Asymptotic stability of solitons for nonlinear hyperbolic equations , Russian Math. Surveys , 68 (2013), no. 2, 283-334.

  38. A.I. Komech, E. Kopylova, S. Kopylov, Nonlinear wave equations with parabolic potentials , J. Spectral Theory , 3 (2013), 1-19. ArXiv 1206.6073.

  39. A.I. Komech, E. Kopylova, Dispersion decay for magnetic Schrödinger equation , J. Funct. Analysis 264 (2013), 735-751. ArXiv 1204.1731.

  40. E. Kopylova, A. Komech, Y. Karlovich, A. Merzon, On the spreading rate of the soliton perturbation for relativistic nonlinear wave equation , Comm. Math. Analysis 14 (2013), no. 2, 95-102.

  41. A.I. Komech, E. Kopylova, D. Stuart, On asymptotic stability of solitary waves for Schrödinger equation coupled to nonlinear oscillator, II, Comm. Pure Appl. Anal. 202 (2012), no. 3, 1063-1079. ArXiv 0807.1878.

  42. E. Kopylova, On long time decay for magnetic Schrödinger and Klein-Gordon equations , Proceedings of the Steklov Institute of Mathematics , 278 (2012), 121-129.

  43. A.I. Komech, E.A. Kopylova, H. Spohn, Scattering of solitons for Dirac equation coupled to a particle , J. Math. Analysis and Appl. 383 (2011), no. 2, 265-290. ArXiv 1012.3109.

  44. A.I. Komech, E.A. Kopylova, On convergence to equilibrium distribution for Dirac equation , Markov Processes Related Fields 17 (2011), no. 4, 523-540. ArXiv 1201.6221.

  45. E.A. Kopylova, A.I. Komech, On asymptotic stability of kink for relativistic Ginzburg-Landau equation , Arch. Rat. Mech. Anal. 202 (2011), no. 2, 213-245. ArXiv 0910.5539.

  46. E. Kopylova, Weighted energy decay for modified Klein-Gordon equation, Comm. Math. Analysis, Conference 03 (2011), 137-152. ArXiv 1009.2649.

  47. E. Kopylova, Weighted energy decay for 1D Dirac equation, Dynamics of PDE 8 (2011), no. 2, 113-125. ArXiv 1102.2157.

  48. E.A. Kopylova, A.I. Komech, On asymptotic stability of moving kink for relativistic Ginzburg-Landau equation , Comm. Math. Physics, 302 (2011), no.1, 225-252. ArXiv 0910.5538.

  49. A.I. Komech, E. Kopylova, Long time decay for 2D Klein-Gordon equation, J. Functional Analysis 259 (2010), no. 2, 477-502.

  50. E. Kopylova, Dispersion estimates for Schrödinger and Klein-Gordon equation , Russian Math. Survey 65 (2010), no. 1, 95-142. http://iopscience.iop.org/0036-0279/65/1/R02/pdf/0036-0279_65_1_R02.pdf

  51. A.I. Komech, E. Kopylova, Weighted energy decay for 1D Klein-Gordon equation, Comm. PDE 35 (2010), 353-374.

  52. E. Kopylova, Dispersion estimates for the 2D wave equation, Russian J. Math. Phys. 17 (2010), no. 2, 226-239.

  53. E. Kopylova, Weighted energy decay for 1D wave equation , J. Math. Anal. Appl 366 (2010), no. 2, 494-505.

  54. A.I. Komech, E. Kopylova, Weighted energy decay for 3D Klein-Gordon equation, J. Differential Equations 248 (2010), no. 3, 501-520. ArXiv 1003.3799. doi:10.1016/j.jde.2009.06.011

  55. E. Kopylova, On dispersion estimates for discrete 3D Schrödinger and Klein-Gordon equation , St. Peretersburg Math. J. 21 (2010), 743-760. ArXiv 0812.0468.

  56. E. Kopylova, On asymptotic stability of solitary waves in discrete Klein-Gordon equation coupled to nonlinear oscillator , Applicable Analysis 89 (2010), no. 9, 1467-1493.

  57. E. Kopylova, On decay of the Schrödinger resolvent , Proceedings of the Steklov Institute of Mathematics 270 (2010), 165-171.

  58. E. Kopylova, On asymptotic stability of solitary waves in discrete Schrödinger equation coupled to a nonlinear oscillator , Nonlinear Analysis Series A: Theory, Methods and Applications 71 (2009), no. 7-8, 3031-3046. ArXiv 0805.3403.

  59. E. Kopylova, Weighted energy decay for 3D wave equation , Asymptotic Analysis 65 (2009), no. 1-2, 1-16.

  60. V. Buslaev, A. Komech, E. Kopylova, D. Stuart, On asymptotic stability of solitary waves in nonlinear Schrödinger equation, Comm. Partial Diff. Eqns 33 (2008), no. 4, 669-705. ArXiv math-ph/0702013.

  61. E. Kopylova, Existence of solitary waves for the discrete Schrödinger equation coupled to a nonlinear oscillator , Russian J. Math. Phys. 15 (2008), no. 4, 486-491.

  62. A. Komech, E. Kopylova, B. Vainberg, On dispersion properties of discrete 2D Schr\"odinger and Klein-Gordon equations , J. Funct. Anal. 254 (2008), no. 8, 2227-2254.

  63. A. Komech, E. Kopylova, M. Kunze, Dispersion estimates for 1D discrete Schrödinger and Klein-Gordon equations, Applicable Analysis 85 (2006), no. 12, 1487-1508.

  64. A. Komech, E.A. Kopylova, Scattering of solitons for Schrödinger equation coupled to a particle, Russian J. Math. Phys. 50 (2006), no. 2, 158-187. arXiv:math/0609649.

  65. A. Komech, E.Kopylova, N.Mauser, On convergence to equilibrium distribution for Schrödinger equation, Markov Processes and Related Fields 11 (2005), no. 1, 81-110.

  66. A. Komech, E.Kopylova, N.Mauser, On convergence to equilibrium distribution for wave equation in even dimensions, Ergodic Theory and Dynamical Systems 24 (2004), 1-30.

  67. T.V. Dudnikova, A.I. Komech, E.A. Kopylova, Yu.M. Suhov, On convergence to equilibrium distribution, I. Klein-Gordon equation with mixing, Comm. Math. Phys. 225 (2002), no. 1, 1-32. ArXiv math-ph/0508042.

  68. E.Kopylova, Stabilization of statistical solutions of the Klein-Gordon equation , Mosc. Univ. Math. Bull. 41 (1986), no. 2, 72-75. http://www.zentralblatt-math.org/zbmath/?index_=1979261&type_=pdf

  69. E.Kopylova, Stabilization of the moment functions of the statistical solution of the wave equation , Mosc. Univ. Math. Bull. 40 (1985), 65-69. http://www.zentralblatt-math.org/zbmath/?index_=2010433&type_=pdf

  70. E.Kopylova, On stabilization of statistical solutions of the Klein-Gordon equation , Russian Math. Survey 40 (1985), no. 5 (245), 240-241 [Russian]. http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=rm&paperid=2767&option_lang=rus