Monographs

  1. A. Komech, Quantum Mechanics: Genesis and Achievements, Springer, Dordrecht, 2013.

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

  3. Yu. Egorov, A. Komech, M. Shubin, Elements of the Modern Theory of Partial Differential Equations, Springer, NY, 1999.

    Textbooks

  4. A.I. Komech, A.A. Komech, Principles of Partial Differential Equations, Springer, 2009.

  5. A. Komech, Practical Solution of Equations of Mathematical Physics, 1993 (2-nd edition) [Russian].

    Lecture notes

  6. A. Komech, Lectures on Elliptic Partial Differential Equations (Method of Pseudodifferential Operators), undergraduate course given at Vienna University during October-December 2006.

  7. A. Komech, On Global Attractors of Hamilton Nonlinear Wave Equations, Lecture Notes of the Max Planck Institute for Mathematics in the Sciences, LN 24/2005, Leipzig, 2005. http://www.mis.mpg.de/preprints/ln/lecturenote-2405-abstr.html

  8. A.I. Komech, A.A. Komech, Book of Practical PDEs, 2006.

Papers

  1. A. Komech, E. Kopylova, On the dispersion decay for crystals in the linearized Schr\"odinger--Poisson model, J. Math. Anal. Appl. 464 (2018), 864-882.

  2. A. Komech, E. Kopylova, On orbital stability of ground states for finite crystals in fermionic Schr\"odinger--Poisson model, SIAM J. Math. Analysis 50 (2018), no. 1, 64--85. Open access.

  3. A. Komech, A. Merzon, Asymptotic completeness of scattering in the nonlinear Lamb system for nonzero mass, Russ. J. Math. Phys. 24 (2017), no. 3, 336--346.

  4. A. Komech, E. Kopylova, H. Spohn, On global attractors and radiation damping for nonrelativistic particle coupled to scalar field, Algebra and Analysis 29 (2017), no. 2, 34--58.

  5. A. Komech, E. Kopylova, On stability of ground states for finite crystals in the Schr\"odinger--Poisson model, J. Math. Phys. 58 (2017), no. 3, 031902-1 -- 031902-18. Open access.

  6. V. Imaykin, A. Komech, H. Spohn, On invariants for the Poincar\'e equations and applications, J. Math. Phys. 58 (2017), no. 1, 012901-1 -- 012901-13. arXiv:1603.03997.

  7. A. Komech, E. Kopylova, On the linear stability of crystals for the Schr\"odinger-Poisson model, J. Stat. Phys. 165 (2016), no. 2, 246-273.

  8. A. Komech, Attractors of nonlinear Hamilton PDEs, Discrete and Continuous Dynamical Systems A 36 (2016), no. 11, 6201-6256.

  9. A. Komech, On crystal ground state in the Schr\"odinger-Poisson model with point ions, Math. Notes 99 (2016), no. 6, 886-894.

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

  11. A. Komech, A.E. Merzon, J.E. De la Paz Mendez, Time-dependent scattering of generalized plane waves by wedge, Mathematical Methods in Applied Sciences 38 (2015), no. 18, 4774-4785. arXiv:1405.7114.

  12. A. Komech, On the Hartree-Fock dynamics in wave-matrix picture, Dynamics of PDE 12 (2015), no. 2, 157-176. arXiv:1407.5208

  13. A. Komech, On dynamical justification of quantum scattering cross section, J. Math. Anal. Appl. 432 (2015), no. 1, 583-602. arXiv:1206.3677

  14. A. Komech, A.E. Merzon, J.E. De la Paz Mendez, On uniqueness and stability of Sobolev's solution in scattering by wedges, Zeitschrift f\"ur angewandte Mathematik und Physik, 66 (2015), no. 5, 2485-2498. http://link.springer.com/article/10.1007/s00033-015-0533-y

  15. A. Komech, E. Kopylova, On the eigenfunction expansion for Hamilton operators, J. Spectral Theory 5 (2015), no.2, 331-361.

  16. A. Komech, A.E. Merzon, J.E. De la Paz Mendez, T. J. Villalba Vega, On the Keller-Blank solution to the scattering problem of pulses by wedges, Mathematical Methods in Applied Sciences, 38 (2015), no. 10, 2035-2040. DOI: 10.1002/mma.3202 http://onlinelibrary.wiley.com/doi/10.1002/mma.3202/

  17. A. Komech, On the crystal ground state in the Schr\"odinger-Poisson model, SIAM J. Math. Anal 47 (2015), no.2, 1001-1021. arXiv:1310.3084

  18. A. Komech, E. Kopylova, Weighted energy decay for magnetic Klein-Gordon equation, J. Applicable Analysis 94 (2015), no. 2, 219-233. arXiv:1309.1759. DOI: 10.1080/00036811.2014.884710

  19. V. Imaykin, A. Komech, H. Spohn, On Lagrangian theory for rotating charge coupled to the Maxwell field, Physics Letters A 379 (2015), no. 1-2, 5-10. arXiv:1206.3641

  20. A.I. Komech, E.A. Kopylova, On eigenfunction expansion of solutions to the Hamilton equations , J. Stat. Phys. 154 (2014), no. 1-2, 503-521. arXiv:1308.0485 DOI 10.1007/s10955-013-0846-1

  21. A.A. Komech, A.I. Komech, On the Titchmarsh convolution theorem for distributions on the circle , Funct. Anal. Appl. 47 (2013), no. 1, 21-26.

  22. A.I. Komech, E.A. Kopylova, S.A. Kopylov, On nonlinear wave equations with parabolic potentials , J. Spec. Theory 3 (2013), no. 4, 485-503. arXiv:1206.6073 DOI 10.4171/JST

  23. A.I. Komech, A.E. Merzon, On asymptotic completeness of scattering in the nonlinear Lamb system II , J. Math. Physic 54 (2013), 012702-012710. arXiv:1205.5850

  24. A.I. Komech, E. Kopylova, Dispersive decay for the magnetic Schr\"odinger equation , J. Funct. Analysis 264 (2013), no. 3, 735-751. arXiv:1006.2618

  25. V. Imaykin, A.I. Komech, B. Vainberg, Scattering of solitons for coupled wave-particle equations , J. Math. Analysis and Appl. 389 (2012), no. 2, 713-740. arXiv:1006.2618

  26. A.I. Komech, E. Kopylova, D. Stuart, On asymptotic stability of solitary waves for Sch\"odinger equation coupled to nonlinear oscillator, II, Comm. Pure Appl. Anal. 202(2012), no. 3, 1063-1079. arXiv:0807.1878

  27. V. Imaykin, A.I. Komech, H. Spohn, Scattering asymptotics for a charged particle coupled to the Maxwell field , J. Math. Physics 52 (2011), no. 4, 042701-042701-33. arXiv:0807.1972

  28. 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

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

  30. 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

  31. A.I. Komech, A.A. Komech, On global attraction to quantum stationary states. Dirac equation with mean field interaction , Commun. Math. Anal. , Conference 3 (2011), 131-136. arXiv:0910.0517

  32. A. Comech, A.I. Komech, Well-posedness and the energy and charge conservation for nonlinear wave equations in discrete space-time , Russ. J. Math. Phys., 18 (2011), no.4, 410-419. arXiv:0910.5538

  33. 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

  34. A.I. Komech, A.A. Komech, Global attraction to solitary waves for nonlinear Dirac equation with mean field interaction , SIAM J. Math. Analysis, 42 (2010), no. 6, 2944-2964. arXiv:0910.0517

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

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

  37. 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

  38. A.I. Komech, A.A. Komech, On global attraction to solitary waves for the Klein-Gordon field coupled to several nonlinear oscillators, J. des Mathematiques Pures et App. 93 (2010), 91-111. arXiv:math/0702660 doi:10.1016/j.matpur.2009.08.011

  39. A.I. Komech, A.A. Komech, On global attraction to solitary waves with mean field interaction Klein-Gordon equation, Annales l'IHP ANL 26 (2009), no. 3, 855-868. arXiv:math/0708.1131

  40. A.I. Komech, A.E. Merzon, On asymptotic completeness of scattering in the nonlinear Lamb system, , J. Math. Physics 50 (2009), 023514-1 --023514-10.

  41. A.I. Komech, A.E. Merzon, Scattering in the nonlinear Lamb system, , Physics Letters A 373 (2009), 1005-1010.

  42. A.I. Komech, A.A. Komech, Global Attraction to Solitary Waves in Models Based on the Klein-Gordon Equation, SIGMA, Symmetry Integrability Geom. Methods Appl. 4 (2008), Paper 010, 23 pages, electronic only. http://www.emis.de/journals/SIGMA/2008/, arXiv:math/0711.0041

  43. 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

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

  45. A.I. Komech, A.A. Komech, Global well-posedness for the Schrodinger equation coupled to a nonlinear oscillator, Russ. J. Math. Phys. 14 (2007), no. 2, 164-173. math.AP/0608780

  46. A.I. Komech, A.E. Merzon, Relation between Cauchy data in the scattering by wedge , Russ. J. Math. Phys. 14 (2007), no. 3, 279-303.

  47. A.I. Komech, A.A. Komech, Global attractor for a nonlinear oscillator coupled to the Klein-Gordon field, Arch. Rat. Mech. Anal.185 (2007), 105-142. arXiv:math.AP/0609013

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

  49. A.I. Komech, A.A. Komech, On global attraction to solitary waves for the Klein-Gordon equation coupled to nonlinear oscillator, C. R., Math., Acad. Sci. Paris 343 (2006), no. 2, 111-114.

  50. V.Imaikin, A. Komech, B. Vainberg, On scattering of solitons for the Klein-Gordon equation coupled to a particle, Comm. Math. Phys. 268 (2006), no. 2, 321-367. arXiv:math.AP/0609205

  51. 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.AP/0609649

  52. M. Freidlin, A. Komech, On metastable regimes in stochastic Lamb system, Journal of Mathematical Physics 47 (2006), 043301-1 -- 043301-12.

  53. A. Komech, A.E.Merzon, Limiting amplitude principle in the diffraction by wedges, Mathematical Methods in Applied Sciences 29 (2006), 1147-1185.

  54. T. Dudnikova, A. Komech, Two-temperature problem for the Klein-Gordon equation, J. Theory Probability and Appl. 50 (2005), no. 4, 675-710. [Russian]. English translation: On two-temperature problem for the Klein-Gordon equation, Theory Prob. Appl. 50 (2006), no. 4, 582-611.))

  55. 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.

  56. T. Dudnikova, A. Komech, On the convergence to a statistical equilibrium in the crystal coupled to a scalar field, Russ. J. Math. Phys. 12 (2005), no. 3, 301-325.

  57. A. Komech, N.J. Mauser, A.E. Merzon, On Sommerfeld representation and uniqueness in diffraction by wedges, Mathematical Methods in Applied Sciences 28 (2005), no. 2, 147-183.

  58. A. Komech, N.J. Mauser, A. Vinnichenko, On attraction to solitons in relativistic nonlinear wave equations, Russ. J. Math. Phys. 11 (2004), no. 3, 289-307.

  59. V.Imaikin, A. Komech, N.J. Mauser, Soliton-type asymptotics for the coupled Maxwell-Lorentz equations, Ann. Inst. Poincaré, Phys. Theor. 5 (2004), 1117-1135.

  60. V.Imaikin, A. Komech, H.Spohn, Rotating charge coupled to the Maxwell field: scattering theory and adiabatic limit, Monatshefte fuer Mathematik 142 (2004), no. 1-2, 143-156.

  61. T.Dudnikova, A. Komech, N.Mauser, On two-temperature problem for harmonic crystals, Journal of Statistical Physics 114 (2004), no. 3/4, 1035-1083.

  62. 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.

  63. A. Komech, On attractor of a singular nonlinear U(1)-invariant Klein-Gordon equation , p. 599-611 in: Proceedings of the 3rd ISAAC Congress, Freie Universitat Berlin, Berlin, 2003.

  64. V.Imaikin, A. Komech, H.Spohn, Scattering theory for a particle coupled to a scalar field, Journal of Discrete and Continuous Dynamical Systems 10 (2003), no. 1&2, 387-396.

  65. V.Imaikin, A. Komech, P.Markowich, Scattering of solitons of the Klein-Gordon equation coupled to a classical particle, Journal of Mathematical Physics 44 (2003), no. 3, 1202-1217.

  66. T.Dudnikova, A. Komech, H.Spohn, On the convergence to statistical equilibrium for harmonic crystals, Journal of Mathematical Physics 44 (2003), no. 6, 2596-2620.

  67. T.Dudnikova, A. Komech, N.Mauser, On the convergence to a statistical equilibrium for the Dirac equation, Russian Journal of Math. Phys. 10 (2003), no. 4, 399-410.

  68. A. Bensoussan, C. Iliine, A. Komech, Breathers for a relativistic nonlinear wave equation, Arch. Rat. Mech. Anal. 165 (2002), 317-345.

  69. 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.

  70. T.V. Dudnikova, A.I. Komech, N.E. Ratanov, Yu.M. Suhov, On convergence to equilibrium distribution, II. Wave equation with mixing, Journal of Statistical Physics 108 (2002), no. 4, 1219-1253.

  71. T. Dudnikova, A. Komech, H. Spohn, On a two-temperature problem for wave equation with mixing, Markov Processes and Related Fields 8 (2002), no. 1, 43-80.

  72. A.Merzon, A. Komech, P.Zhevandrov, A method of complex characteristics for elliptic problems in angles and its applications, Translations. Series 2. American Mathematical Society. 206, American Mathematical Society (AMS), Providence, RI, 2002.

  73. T. Dudnikova, A. Komech, H. Spohn, Energy-momentum relation for solitary waves of relativistic wave equation, Russian Journal Math. Phys. 9 (2002), no. 2, 153-160.

  74. V.Imaikin, A. Komech, H.Spohn, Soliton-like asymptotics and scattering for a particle coupled to Maxwell field, Russian Journal of Mathematical Physics 9 (2002), no. 4, 428-436.

  75. A. Komech, H.Spohn, Long-time asymptotics for the coupled Maxwell-Lorentz equations, Communications in Partial Differential Equations 25 (2000), no. 3\&4, 559-584.

  76. A. Komech, Attractors of non-linear Hamiltonian one-dimensional wave equations, Russian Math. Surv. 55 (2000), no. 1, 43-92.

  77. A. Komech, On transitions to stationary states in one-dimensional nonlinear wave equations, Arch. Rat. Mech. Anal. 149 (1999), no. 3, 213-228.

  78. A. Komech, M. Kunze, H. Spohn, Effective Dynamics for a mechanical particle coupled to a wave field, Comm. Math. Phys. 203 (1999), 1-19.

  79. A. Komech, P. Joly, O. Vacus, On transitions to stationary states in a Maxwell-Landau- Lifschitz-Gilbert system, SIAM J. Math. Anal. 31 (1999), no. 2, 346-374.

  80. A. Komech, On transitions to stationary states in Hamiltonian nonlinear wave equations, Phys. Letters A 241 (1998), 311-322.

  81. A. Komech, H. Spohn, Soliton-like asymptotics for a classical particle interacting with a scalar wave field, Nonlinear Analysis 33 (1998), no. 1, 13-24.

  82. A. Komech, H. Spohn, M. Kunze, Long-Time Asymptotics for a Classical Particle Interacting with a Scalar Wave Field , Comm. Partial Dif. Equns. 22 (1997), no.1/2, 307-335.

  83. A. Komech, B. Vainberg, On asymptotic stability of stationary solutions to nonlinear wave and Klein-Gordon equations, , Arch. Ration. Mech. Anal. 134 (1996), no.3, 227-248.

  84. A. Komech, On stabilization of string-nonlinear oscillator interaction, J. Math. Anal. Appl. 196 (1995), 384-409.

  85. A. Komech, Elliptic boundary value problems on manifolds with a piecewise smooth boundary , Math. USSR Sbornik 21 (1973), no.1, 91-135.