Kalyakin, Leonid Anatol'evich

Total publications: 84 (81)
in MathSciNet: 64 (62)
in zbMATH: 50 (50)
in Web of Science: 41 (40)
in Scopus: 37 (37)
Cited articles: 55
Citations in Math-Net.Ru: 250
Citations in Web of Science: 150
Citations in Scopus: 97
Presentations: 1

Number of views:
This page:2416
Abstract pages:12996
Full texts:3428
Kalyakin, Leonid Anatol'evich
Doctor of physico-mathematical sciences (1988)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 8.07.1947
Phone: +7 (347) 273 33 42
Fax: +7 (347) 272 59 36
Keywords: asymptotics, small parameter, differential equations, resonance.
UDC: 517.928.226, 517.946.9, 517.948, 517.956, 517.956.226, 517.958.530.145.7, 518, 519.634
MSC: 35C20, 35B40, 35L40, 35L70, 35Q55


Asymptotic solutions of nonlinear differential equations.


1969 Mathematician diploma, Ural State University, Sverdlovsk. From 1968 work in the Institute of Mathematics and Mechanics, Ural Branch of RAS, Sverdlovsk. 1975 PhD, thesis "Methods of solving unstable problems", Ural State University, Sverdlovsk. From 1978 work in the Department of Physics and Mathematics, Bashkir Scientific center of RAS. From 1987 Head of the Department of Differential Equations, Institute of Mathematics, Ufa Scientific Center of RAS. 1989 Doctor's degree, thesis "Long-wave asymptotics for the solutions of the systems of nonlinear equations", Institute of Mathematics and Mechanics, Ural Branch of RAS, Sverdlovsk. 1992 Professor of the Department of differential Equations, Bashkir State University, 2000 Soros' Professor, supervisor of six philosophy doctors in differential equations. For many years gives the lecture courses on differential equations and mathematical physics at the Faculty of Mathematics, BSU. Scientific interests are concerned to the application of asymptotic methods for solving nonlinear problems of mathematical physics. Author of more than 80 publications. Co-author of papers concerning to application of asymptotic methods in chemical kinetics, fluid dynamics, written in active collaboration with chemists, physicists and mechanicians.

Main publications:
  1. L. A. Kalyakin, “Long wave asymptotics. Integrable equations as asymptotic limits of non-linear systems”, Russian Math. Surveys, 44:5 (1989), 1–34
  2. L. A. Kalyakin, “Asymptotic analysis of autoresonance models”, Russian Math. Surveys, 63:5 (2008), 791–857
List of publications on Google Scholar
List of publications on ZentralBlatt

Full list of publications:
| by years | by types | by times cited in WoS | by times cited in Scopus | scientific publications | common list |

1. L. A. Kalyakin, “Resonance capture in a system of two oscillators near equilibrium”, Theoret. and Math. Phys., 194:3 (2018), 331–346  mathnet  crossref  crossref  isi  elib  scopus
2. L. A. Kalyakin, “Analysis of a Mathematical Model for Nuclear Spins in an Antiferromagnet”, Russian Journal of Nonlinear Dynamics, 14:2 (2018), 217–234  mathnet  crossref  elib
3. J. A. Baimova, I, Evazzade, L. A. Kalyakin, S. V. Dmitriev and K. Zhou, “Dehydrogenation of graphane by external driving”, IOP Conf. Series: Materials Science and Engineering, 447:conference 1 (2018), 012011 , 5 pp.  crossref  scopus
4. L. A. Kalyakin, “Capture and holding of resonance far from equilibrium”, Ufa Math. J., 10:4 (2018), 64–76  mathnet  crossref  isi

5. L. A. Kalyakin, “Asymptotic analysis of the model of gyromagnetic autoresonance”, Comput. Math. Math. Phys., 57:2 (2017), 281–296  mathnet  crossref  crossref  isi (cited: 2)  elib  scopus (cited: 1)
6. L. A. Kalyakin, “Adiabatic approximation for a Model of Cyclotron Motion”, Math. Notes, 101:5 (2017), 850–862  mathnet  crossref  crossref  mathscinet  isi  elib  scopus
7. L. A. Kalyakin, “Painleve II equation as a model of a resonant interaction of oscillators”, Trudy Inst. Mat. i Mekh. UrO RAN, 23, no. 2, 2017, 104–116  mathnet  crossref  isi  elib
8. Kalyakin L.A, “Adiabatic approximation in a resonance capture problem”, Ufa Mathematical Journal, 9:3 (2017), 61-75  mathnet  crossref  mathscinet  isi  elib  scopus
9. S. A. Kordyukova, L. A. Kalyakin, “On a double boundary layer in a nonlinear boundary value problem”, Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 129–146  mathnet  crossref  mathscinet  isi  elib  scopus

10. L. A. Kalyakin, “Stability of the autoresonance in a dissipative system”, Russian Journal of Mathematical Physics, 23:1 (2016), 77–87  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 1)
11. L. A. Kalyakin, “Stability of equilibrium with respect to a white noise”, Proc. Steklov Inst. Math. (Suppl.), 295, suppl. 1 (2016), 68–77  mathnet  crossref  mathscinet  elib

12. L. A. Kalyakin, “Lyapunov Functions in Justification Theorems for Asymptotics”, Math. Notes, 98:5 (2015), 752–764  mathnet  crossref  crossref  mathscinet  isi  elib  scopus
13. L.A.Kalyakin, “Asimptoticheskii analiz modeli tsiklotronnogo giromagnitnogo avtorezonansa”, Vestnik chelyabinskogo gosudarstvennogo universiteta, 22 (377), Fizika:21 (2015), 68-74  elib

14. L. A. Kalyakin, “Phantom asymptotic solutions”, Ufa Math. Journal, 6:2 (2014), 44–65  mathnet  crossref  elib  elib  scopus (cited: 1)
15. L. A. Kalyakin, “Synchronization in a nonisochronous nonautonomous system”, Theoret. and Math. Phys., 181:2 (2014), 1339–1348  mathnet  crossref  crossref  mathscinet  adsnasa  isi (cited: 1)  elib  elib  scopus (cited: 2)
16. L. A. Kalyakin, “Lyapunov functions in barriers for parabolic equations and in stability problems with respect to “white noise””, Russian Journal of Mathematical Physics, 21:4 (2014), 472–483  crossref  mathscinet  zmath  isi (cited: 2)
17. L. A. Kalyakin, “Existence Theorems and Estimates of Solutions for Equations of Principal Resonance”, Journal of Mathematical Sciences, 200:1 (2014), 82-95  crossref  mathscinet  zmath  scopus (cited: 2)
18. L Kalyakin, “Stability under persistent perturbation by white noise”, Journal of Physics: Conference Series, 482 (2014), 012019 , 7 pp.  crossref  mathscinet  isi (cited: 4)

19. L. A. Kalyakin, “Stability of nondissipative systems under random perturbations that are small in the mean”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 2, 2013, 170–178  mathnet  mathscinet  elib
20. L. A. Kalyakin, O. A. Sultanov, “Stability of autoresonance models”, Differential Equations, 49:3 (2013), 267–281  crossref  mathscinet  zmath  elib

21. L. A. Kalyakin, “Stability of Nondissipative Systems under Persistent Random Perturbations”, Math. Notes, 92:1 (2012), 136–139  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 2)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 2)

22. L. A. Kalyakin, “Analysis of the Bloch equations for the nuclear magnetization model”, Proceedings of the Steklov Institute of Mathematics, 281:Suppl. 1 (2013), 64–81  mathnet  crossref  isi  elib  scopus (cited: 1)

23. L. A. Kalyakin, “Asymptotic analysis of the surfing acceleration model”, Ufimsk. Mat. Zh., 4:2 (2012), 101–113  mathnet  elib

24. L. A. Kalyakin, O. A. Sultanov, M. A. Shamsutdinov, “Asymptotic analysis of a model of nuclear magnetic autoresonance”, Theoret. and Math. Phys., 167:3 (2011), 762–771  mathnet  crossref  crossref  mathscinet  adsnasa  isi (cited: 2)  elib  scopus (cited: 3)
25. A.T. Kharisov, L.A. Kalyakin, M.A. Shamsutdinov, “Autoresonance Excitation of Nonlinear Oscillations of Magnetization and Domain Walls in Ferromagnets”, Solid State Phenomena, 168-169 (2011), 77-80  crossref  isi
26. V.N. Nazarov, L.A. Kalyakin, M.A. Shamsutdinov, “Autoresonance Parametric Excitation of the Magnetic Breather in a Uniaxial Ferromagnet”, Solid State Phenomena, 168-169 (2011), 81-84  crossref  isi (cited: 1)
27. O. A. Sultanov, L. A. Kalyakin, “Averaging of the Bloch equations”, Vestnik Chelyabinsk. Gos. Univ., 2011, no. 14, 107–112  mathnet  mathscinet  elib
28. L. A. Kalyakin, V. Yu. Novokshenov, I. T. Habibullin, E. G. Ekomasov, A. T. Kharisov, “In memory of Miniakhat Asgatovich Shamsutdinov”, Ufimsk. Mat. Zh., 3:1 (2011), 122–123  mathnet

29. L. A. Kalyakin, “Analysis of a synchronization model in an anisochronous system”, Comput. Math. Math. Phys., 50:8 (2010), 1338–1349  mathnet  crossref  mathscinet  adsnasa  isi (cited: 1)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 1)

30. L. A. Kalyakin, M. A. Shamsutdinov, “Autoresonant asymptotics in an oscillating system with weak dissipation”, Theoret. and Math. Phys., 160:1 (2009), 960–967  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 8)  elib
31. L. A. Kalyakin, “Averaging method for the problems on asymptotics at infinity”, Ufimsk. Mat. Zh., 1:2 (2009), 29–52  mathnet  zmath  elib

32. L. A. Kalyakin, “Asymptotic analysis of autoresonance models”, Russian Math. Surveys, 63:5 (2008), 791–857  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 35)  elib (cited: 19)  elib (cited: 19)  scopus (cited: 26)

33. L. A. Kalyakin, M. A. Shamsutdinov, “Adiabatic approximations for Landau–Lifshitz equations”, Proc. Inst. Math. Mech., 259, suppl. 2 (2007), S124–S140  mathnet  crossref  elib  scopus (cited: 3)
34. E. M. Maslov, L. A. Kalyakin, A. G. Shagalov, “Breather resonant phase locking by an external perturbation”, Theoret. and Math. Phys., 152:2 (2007), 1173–1182  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 7)  elib  scopus (cited: 6)
35. R. N. Garifullin, L. A. Kalyakin, M. A. Shamsutdinov, “Autoresonance excitation of a breather in weak ferromagnetics”, Comput. Math. Math. Phys., 47:7 (2007), 1158–1170  mathnet  crossref  mathscinet  elib (cited: 6)  elib (cited: 6)  scopus (cited: 10)

36. L. A. Kalyakin, Yu. Yu. Bagderina, “Asymptotics for the solution of averaged equations for the system of coupled oscillators”, J. Math. Sci., 151:1 (2008), 2699–2709  mathnet  crossref  mathscinet  zmath  elib (cited: 1)  elib (cited: 1)  scopus (cited: 1)

37. L. A. Kalyakin, “Intermediate asymptotics for solutions to the degenerate principal resonance equations”, Comput. Math. Math. Phys., 46:1 (2006), 79–89  mathnet  crossref  mathscinet  zmath  elib (cited: 1)  elib (cited: 1)  scopus (cited: 2)

38. L. A. Kalyakin, Yu. Yu. Bagderina, “Asymptotics of Bounded-at-Infinity Solutions of the Principal Resonance Equation”, Math. Notes, 78:1 (2005), 76–87  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 1)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 1)
39. L. A. Kalyakin, “Resonance Capture in a Nonlinear System”, Theoret. and Math. Phys., 144:1 (2005), 944–951  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 2)  elib  scopus (cited: 2)
40. L. Kalyakin, “Asymptotic analysis of a model of autoresonance”, International Conference on Control and Synchronzation of Dynamical Systems (OCTOBER 4-7 2005 León Gto.México), Journal of Physics: Conference Series, 23, 2005, 17–22  crossref  scopus (cited: 1)

41. L. A. Kalyakin, “Asymptotic Solution of the Threshold Phenomenon Problem for the Principal Resonance Equations”, Differ. Equ., 40:6 (2004), 780–788  mathnet  crossref  mathscinet

42. L. A. Kalyakin, “Averaging in the Autoresonance Model”, Math. Notes, 73:3 (2003), 414–418  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 8)  scopus (cited: 4)
43. L. A. Kalyakin, “Justification of asymptotic expansions for the principal resonance equations”, Proc. Inst. Math. Mech., 2003no. , suppl. 1, S108–S122  mathnet  mathscinet  zmath  elib
44. L. A. Kalyakin, “Asymptotic Behavior of Solutions of Equations of Main Resonance”, Theoret. and Math. Phys., 137:1 (2003), 1476–1484  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 7)  scopus (cited: 6)
45. V. M. Babich, L. A. Kalyakin, M. D. Ramazanov, N. Kh. Rozov, “Arlen Mikhailovich Il'in (on the occasion of the 70th anniversary)”, Proc. Inst. Math. Mech., 2003no. , suppl. 1, S1–S7  mathnet  mathscinet  zmath  elib

46. L. A. Kalyakin, “Asymptotic Solution of the Autoresonance Problem”, Theoret. and Math. Phys., 133:3 (2002), 1684–1691  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 2)  scopus (cited: 2)
47. V. M. Babich, R. R. Gadyl'shin, A. R. Danilin, S. Yu. Dobrokhotov, V. A. Il'in, L. A. Kalyakin, E. F. Mishchenko, V. Yu. Novokshenov, Yu. S. Osipov, M. D. Ramazanov, N. Kh. Rozov, V. A. Sadovnichii, “Arlen Mikhailovich Il'in (A tribute in honor of his 70th birthday)”, Differ. Equ., 38:8 (2002), 1075–1080  mathnet  crossref  mathscinet

48. L. A. Kalyakin, “Weak perturbations of solutions with movable singularities”, Proc. Inst. Math. Mech., 2001no. , suppl. 1, S85–S106  mathnet  mathscinet  zmath  elib
49. L. A. Kalyakin, “Perturbation of Solutions with Moving Singularities”, Theoret. and Math. Phys., 127:3 (2001), 751–759  mathnet  crossref  crossref  mathscinet  zmath  isi  scopus

50. L. A. Kalyakin, “Asymptotic decay of solutions of the Liouville equation under perturbations”, Math. Notes, 68:2 (2000), 173–184  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus

51. L. A. Kalyakin, “Perturbation of a singular solution to the Liouville equation”, Theoret. and Math. Phys., 118:3 (1999), 307–313  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 2)  scopus (cited: 2)
52. L. A. Kalyakin, M. M. Shakiryanov, “Asymptotic behavior of the solution of the Cauchy problem for the two-dimensional homogeneous wave equation”, Differ. Equ., 35:9 (1999), 1307–1309  mathnet  mathscinet

53. L. A. Kalyakin, “Week interaction of the perturbed Korteveg–de Vries solutions”, Fundam. Prikl. Mat., 4:4 (1998), 1179–1205  mathnet  mathscinet  zmath

54. L. A. Kalyakin, S. I. Maslennikov, “Method of the asymptotic approximations to the mathematical analysis of the chemical kinetic problem”, Matem. Mod., 9:8 (1997), 60–69  mathnet  mathscinet  zmath
55. L. A. Kalyakin, V. A. Lazarev, “Perturbation of the two-soliton solution of the KdV equation”, Theoret. and Math. Phys., 112:1 (1997), 866–874  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 2)  elib (cited: 2)  scopus (cited: 2)

56. A. I. Bobenko, A. M. Il'in, S. Yu. Dobrokhotov, A. R. Its, L. A. Kalyakin, V. B. Matveev, V. Yu. Novokshenov, A. B. Shabat, “Ramil' Faritovich Bikbaev (obituary)”, Russian Math. Surveys, 51:1 (1996), 129–133  mathnet  crossref  crossref  mathscinet  adsnasa  isi

57. L. A. Kalyakin, “Asymptotics of the first correction in the perturbation of the $N$-soliton solution to the KdV equation”, Math. Notes, 58:2 (1995), 814–823  mathnet  crossref  mathscinet  zmath  isi (cited: 2)
58. L. A. Kalyakin, “On the problem of first correction in soliton perturbation theory”, Sb. Math., 186:7 (1995), 977–1002  mathnet  crossref  mathscinet  zmath  isi

59. L. A. Kalyakin, S. G. Glebov, “On the solvability of nonlinear equations of Shrödinger type in the class of rapidly oscillating functions”, Math. Notes, 56:1 (1994), 673–678  mathnet  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 1)

60. L. A. Kalyakin, “Asymptotics of a double integral of Fourier type in the theory of soliton perturbation”, Differ. Equ., 29:6 (1993), 867–880  mathnet  mathscinet

61. L. A. Kalyakin, “Perturbation of the Korteweg–de Vries soliton”, Theoret. and Math. Phys., 92:1 (1992), 736–747  mathnet  crossref  mathscinet  zmath  isi (cited: 10)  scopus (cited: 10)

62. L. A. Kalyakin, “Asymptotics of an integral that arises in the theory of perturbations of KdV solitons”, Math. Notes, 50:5 (1991), 1114–1122  mathnet  crossref  mathscinet  zmath  isi (cited: 2)  scopus (cited: 2)

63. L. A. Kalyakin, “The method of matching in a problem on long-wave modulation of nonlinear two-dimensional waves with dispersion”, Tr. Mosk. Mat. Obs., 53, MSU, M., 1990, 3–41  mathnet  mathscinet  zmath

64. L. A. Kalyakin, “Long wave asymptotics. Integrable equations as asymptotic limits of non-linear systems”, Russian Math. Surveys, 44:1 (1989), 3–42  mathnet  crossref  mathscinet  zmath  adsnasa  isi (cited: 41)

65. L. A. Kalyakin, “Local resonance in a weakly nonlinear problem”, Mat. Zametki, 44:5 (1988), 697–699  mathnet  zmath
66. L. A. Kalyakin, “Asymptotic transitions from discrete to continuous models”, Theoret. and Math. Phys., 76:3 (1988), 891–894  mathnet  crossref  mathscinet  zmath  isi (cited: 2)  scopus (cited: 2)
67. L. A. Kalyakin, “Asymptotic decay of a one-dimensional wave packet in a nonlinear dispersive medium”, Math. USSR-Sb., 60:2 (1988), 457–483  mathnet  crossref  mathscinet  zmath

68. L. A. Kalyakin, Differ. Uravn., 23:4 (1987), 696–705  mathnet  mathscinet

69. L. A. Kalyakin, “Asymptotic integration of a perturbed hyperbolic system of equations in the class of conditionally periodic functions”, Tr. Mosk. Mat. Obs., 49, MSU, M., 1986, 56–70  mathnet  mathscinet  zmath

70. L. A. Kalyakin, “The asymptotic behaviour of the solution of a hyperbolic system of equations with a non-linear perturbation”, Russian Math. Surveys, 39:5 (1984), 277–278  mathnet  crossref  mathscinet  zmath  adsnasa  isi (cited: 1)

71. L. A. Kalyakin, “Long wave asymptotics of asolution of a hyperbolic system of equations”, Math. USSR-Sb., 52:1 (1985), 91–114  mathnet  crossref  mathscinet  zmath

72. L. A. Kalyakin, Differ. Uravn., 20:2 (1984), 351–353  mathnet  zmath

73. L. A. Kalyakin, “An asymptotic expansion of the solution of a degenerate parabolic equation with a small parameter”, Russian Math. Surveys, 38:1 (1983), 194–195  mathnet  crossref  mathscinet  zmath  adsnasa  isi
74. L. A. Kalyakin, Differ. Uravn., 19:11 (1983), 1991–1992  mathnet  mathscinet  zmath
75. L. A. Kalyakin, Differ. Uravn., 19:4 (1983), 628–644  mathnet  mathscinet  zmath

76. L. A. Kalyakin, Differ. Uravn., 18:10 (1982), 1724–1738  mathnet  mathscinet  zmath

77. L. A. Kalyakin, Differ. Uravn., 15:4 (1979), 668–680  mathnet  mathscinet  zmath
78. L. A. Kalyakin, Differ. Uravn., 15:10 (1979), 1873–1887  mathnet  mathscinet

79. L. A. Kalyakin, “On approximate methods of solving nonlinear boundary value problems with a small parameter”, Math. USSR-Sb., 28:4 (1976), 491–500  mathnet  crossref  mathscinet  zmath  isi

80. L. A. Kalyakin, Differ. Uravn., 10:9 (1974), 1684–1691  mathnet  mathscinet  zmath

81. L. A. Kalyakin, “Approximate solution of certain unstable problems”, Izv. Vyssh. Uchebn. Zaved. Mat., 1972, no. 10, 41–45  mathnet  mathscinet  zmath
82. L. A. Kalyakin, “The approximate solution of ill-posed problems in normed spaces”, U.S.S.R. Comput. Math. Math. Phys., 12:5 (1972), 104–122  mathnet  crossref  mathscinet  zmath  scopus

83. L. A. Kalyakin, “Galerkin's method for equations with a small parameter in the highest order derivatives”, Math. USSR-Sb., 14:4 (1971), 525–536  mathnet  crossref  mathscinet  zmath

84. L. A. Kalyakin, “Ritz method for equations with small parameters for higher derivatives”, Math. Notes, 6:1 (1969), 513–516  mathnet  crossref  mathscinet  zmath  scopus

Presentations in Math-Net.Ru
1. Asymptotic analysis of autoresonance in the system with small dissipation
L. A. Kalyakin
International conference "Geometrical Methods in Mathematical Physics"
December 14, 2011 16:00   

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