Monographs

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

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

Papers

  1. 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.

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

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

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

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

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

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

  8. 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.

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

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

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

  12. 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.

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

  14. 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

  15. 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

  16. 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

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

  18. 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

  19. 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

  20. 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

  21. 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

  22. 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

  23. 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

  24. 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

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

  26. A. Komech, E. Kopylova, Weighted energy decay for magnetic Klein-Gordon equations , Applicable Analysis . 94 (2015), no. 2, 219-233. ArXiv 1308.0485

  27. 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

  28. 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

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

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

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

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

  33. 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.

  34. 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.

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

  36. 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.

  37. 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.

  38. 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.

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

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

  41. 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.

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

  43. 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

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

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

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

  47. 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

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

  49. 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.

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

  51. 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.

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

  53. 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.

  54. 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.

  55. 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.

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

  57. 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.

  58. 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.

  59. 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.

  60. 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.

  61. 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

  62. 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

  63. 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