Asymptotic solutions of nonlinear differential equations.
Biography
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:
L. A. Kalyakin, “Long wave asymptotics. Integrable equations as asymptotic limits of non-linear systems”, Russian Math. Surveys, 44:5 (1989), 1–34
L. A. Kalyakin, “Asymptotic analysis of autoresonance models”, Russian Math. Surveys, 63:5 (2008), 791–857
L. A. Kalyakin, “Stability of a Traveling Wave on a Saddle-Node Trajectory”, Math. Notes, 115:6 (2024), 931–942
2.
L. A. Kalyakin, E. G. Ekomasov, “Simulation of Domain Walls: Simple Waves in the Magnetodynamics Equation”, Computational Mathematics and Mathematical Physics, 64 (2024), 85–98
L. A. Kalyakin, Mat. Zametki, 116:6 (2024), 900–917 (to appear)
2023
4.
L. A. Kalyakin, “Perturbation of a simple wave in a domain wall model”, Proc. Steklov Inst. Math. (Suppl.), 321, suppl. 1 (2023), S90–S100
5.
L. A. Kalyakin, “Perturbation of a simple wave: from simulation to asymptotics”, Ufa Math. J., 15:3 (2023), 54–68
2022
6.
L. A. Kalyakin, “Asymptotics of a dynamic saddle-node bifurcation for the nuclear spin model in an antiferromagnet”, Trudy Inst. Mat. i Mekh. UrO RAN, 28, no. 1, 2022, 111–126
7.
L. A. Kalyakin, “Asymptotics of Andronov–Hopf Dynamic Bifurcations”, Journal of Mathematical Sciences, 260 (2022), 756–773
Kalyakin L. A., “Asymptotics of Dynamical Saddle-node Bifurcations”, Russian Journal of Nonlinear Dynamics, 18:1 (2022), 119-135http://nd.ics.org.ru/nd220108/
9.
L. A. Kalyakin, “Perturbation of a Simple Wave in a System with Dissipation”, Math. Notes, 112:4 (2022), 549–560
10.
L. A. Kalyakin, “Asymptotics of the solution for the system of Landau–Lifsitz equations under saddle-node dynamical bifurcation”, St. Petersburg Math. J., 33:2 (2022), 223–242
2021
11.
L. A. Kalyakin, “Asymptotics of the Solution of a Variational Problem on a Large Interval”, Math. Notes, 110:5 (2021), 687–699
12.
L. A. Kalyakin, A.K.Zvezdin, Z.V.Gareeva, “Ustoichivost asimptoticheskogo priblizheniya v modelyakh multiferroikov”, Problemy matematicheskogo analiza, 2021, no. 108, 83-97
13.
L. A. Kalyakin, A. K. Zvezdin, and Z. V. Gareeva, “Stability of Asymptotic Approximation in Models of Multiferroics”, JOURNAL OF MATHEMATICAL SCIENCES, 255:4 (2021), 444-458
2020
14.
L. A. Kalyakin, A. K. Zvezdin, Z. V. Gareeva, “Asymptotic analysis of a multiferroic model”, Theoret. and Math. Phys., 203:1 (2020), 457–468
15.
Z. V. Gareeva, L. A. Kalyakin, I. R. Kayumov, A. K. Zvezdin, “SPIN-PEREORIENTATsIONNYE PEREKhODY V MULTIFERROIKAKh S TsIKLOIDALNYM SPINOVYM UPORYaDOChENIEM”, FIZIKA METALLOV I METALLOVEDENIE, 121:4 (2020), 352-358
L. A. Kalyakin, “Asymptotics of Solutions of the Nonlinear Oscillator Model with Natural Boundary Conditions”, JOURNAL OF MATHEMATICAL SCIENCES, 247, no. 6, 877-887
2020
17.
Z. V. Gareeva, A. K. Zvezdin,L. A. Kalyakin,T. T. Gareev, “Dzyaloshinskii – Moriya interaction, epitaxial strains, phase transitions in multiferroics with cycloidal structure”, Journal of Magnetism and Magnetic Materials, 515 (2020), 167255 , 14 pp.
18.
GAREEVA Z.V.,KALYAKIN L.A.,KAYUMOV I.R., ZVEZDIN A.K, “SPIN-REORIENTATION TRANSITIONS IN MULTIFERROICS WITH CYCLOIDAL SPIN ORDERING”, THE PHYSICS OF METALS AND METALLOGRAPHY, 121:4 (2020), 310-315
L. A. Kalyakin, “On the frequency of a nonlinear oscillator”, Differential Equations, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 163, VINITI, Moscow, 2019, 15–24
20.
L. A. Kalyakin, “Capture and Keeping of a Resonance near Equilibrium”, Russian Journal of Mathematical Physics, 26:2 (2019), 152-167https://link.springer.com/journal/11503/26/2
21.
L. A. Kalyakin, “Asymptotics of the Solution of a Differential Equation in a Saddle–Node Bifurcation”, Computational Mathematics and Mathematical Physics, 59:9 (2019), 1454–1469. (to appear)
2018
22.
L. A. Kalyakin, “Resonance capture in a system of two oscillators near equilibrium”, Theoret. and Math. Phys., 194:3 (2018), 331–346
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.
25.
L. A. Kalyakin, “Capture and holding of resonance far from equilibrium”, Ufa Math. J., 10:4 (2018), 64–76
2017
26.
L. A. Kalyakin, “Asymptotic analysis of the model of gyromagnetic autoresonance”, Comput. Math. Math. Phys., 57:2 (2017), 281–296
27.
L. A. Kalyakin, “Adiabatic approximation for a Model of Cyclotron Motion”, Math. Notes, 101:5 (2017), 850–862
2018
28.
L. A. Kalyakin, “Painleve II equation as a model of a resonant interaction of oscillators”, Proc. Steklov Inst. Math. (Suppl.), 303, suppl. 1 (2018), 124–135
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
2016
31.
L. A. Kalyakin, “Stability of the autoresonance in a dissipative system”, Russian Journal of Mathematical Physics, 23:1 (2016), 77–87
L. A. Kalyakin, “Phantom asymptotic solutions”, Ufa Math. Journal, 6:2 (2014), 44–65
36.
L. A. Kalyakin, “Synchronization in a nonisochronous nonautonomous system”, Theoret. and Math. Phys., 181:2 (2014), 1339–1348
37.
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), 472–483http://link.springer.com/article/10.1134/S1061920814040050
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
L. A. Kalyakin, “Stability of Nondissipative Systems under Persistent Random Perturbations”, Math. Notes, 92:1 (2012), 136–139
2013
43.
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
2012
44.
L. A. Kalyakin, “Asymptotic analysis of the surfing acceleration model”, Ufimsk. Mat. Zh., 4:2 (2012), 101–113
2011
45.
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
46.
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), 77-80http://www.scientific.net/SSP.168-169.77
47.
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), 81-84http://www.scientific.net/SSP.168-169.81
O. A. Sultanov, L. A. Kalyakin, “Averaging of the Bloch equations”, Vestnik Chelyabinsk. Gos. Univ., 2011, no. 14, 107–112
49.
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
2010
50.
L. A. Kalyakin, “Analysis of a synchronization model in an anisochronous system”, Comput. Math. Math. Phys., 50:8 (2010), 1338–1349
2009
51.
L. A. Kalyakin, M. A. Shamsutdinov, “Autoresonant asymptotics in an oscillating system with weak dissipation”, Theoret. and Math. Phys., 160:1 (2009), 960–967
52.
L. A. Kalyakin, “Averaging method for the problems on asymptotics at infinity”, Ufimsk. Mat. Zh., 1:2 (2009), 29–52
2008
53.
L. A. Kalyakin, “Asymptotic analysis of autoresonance models”, Russian Math. Surveys, 63:5 (2008), 791–857
2007
54.
L. A. Kalyakin, M. A. Shamsutdinov, “Adiabatic approximations for Landau–Lifshitz equations”, Proc. Inst. Math. Mech., 259, suppl. 2 (2007), S124–S140
55.
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
56.
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
2008
57.
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
2006
58.
L. A. Kalyakin, “Intermediate asymptotics for solutions to the degenerate principal resonance equations”, Comput. Math. Math. Phys., 46:1 (2006), 79–89
2005
59.
L. A. Kalyakin, Yu. Yu. Bagderina, “Asymptotics of Bounded-at-Infinity Solutions of the Principal Resonance Equation”, Math. Notes, 78:1 (2005), 76–87
60.
L. A. Kalyakin, “Resonance Capture in a Nonlinear System”, Theoret. and Math. Phys., 144:1 (2005), 944–951
61.
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
L. A. Kalyakin, “Asymptotic Solution of the Threshold Phenomenon Problem for the Principal Resonance Equations”, Differ. Equ., 40:6 (2004), 780–788
2003
63.
L. A. Kalyakin, “Averaging in the Autoresonance Model”, Math. Notes, 73:3 (2003), 414–418
64.
L. A. Kalyakin, “Justification of asymptotic expansions for the principal resonance equations”, Proc. Inst. Math. Mech., 2003no. , suppl. 1, S108–S122
65.
L. A. Kalyakin, “Asymptotic Behavior of Solutions of Equations of Main Resonance”, Theoret. and Math. Phys., 137:1 (2003), 1476–1484
66.
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
2002
67.
L. A. Kalyakin, “Asymptotic Solution of the Autoresonance Problem”, Theoret. and Math. Phys., 133:3 (2002), 1684–1691
68.
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
2001
69.
L. A. Kalyakin, “Weak perturbations of solutions with movable singularities”, Proc. Inst. Math. Mech., 2001no. , suppl. 1, S85–S106
70.
L. A. Kalyakin, “Perturbation of Solutions with Moving Singularities”, Theoret. and Math. Phys., 127:3 (2001), 751–759
2000
71.
L. A. Kalyakin, “Asymptotic decay of solutions of the Liouville equation under perturbations”, Math. Notes, 68:2 (2000), 173–184
72.
G. T. Bulgakova, L. A. Kalyakin, M. M. Khasanov, “Stability of filtration of a gas–liquid mixture”, J. Appl. Mech. Tech. Phys., 41:6 (2000), 1029–1035
1999
73.
L. A. Kalyakin, “Perturbation of a singular solution to the Liouville equation”, Theoret. and Math. Phys., 118:3 (1999), 307–313
74.
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
1998
75.
L. A. Kalyakin, “Week interaction of the perturbed Korteveg–de Vries solutions”, Fundam. Prikl. Mat., 4:4 (1998), 1179–1205
1997
76.
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
77.
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
1996
78.
L. A. Kalyakin, M. M. Shakiryanov, “Well-posedness of the Goursat–Cauchy problem for a system of equations of Davey–Stewartson type”, Dokl. Akad. Nauk, 346:4 (1996), 445–447
79.
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
1995
80.
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
81.
L. A. Kalyakin, “On the problem of first correction in soliton perturbation theory”, Sb. Math., 186:7 (1995), 977–1002
1994
82.
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
83.
A. M. Il'in, L. A. Kalyakin, “Perturbation of finite-soliton solutions of the Korteweg–de Vries equation”, Dokl. Akad. Nauk, 336:5 (1994), 595–598
1993
84.
L. A. Kalyakin, “Asymptotics of a double integral of Fourier type in the theory of soliton perturbation”, Differ. Equ., 29:6 (1993), 867–880
1992
85.
L. A. Kalyakin, “Perturbation of the Korteweg–de Vries soliton”, Theoret. and Math. Phys., 92:1 (1992), 736–747
1991
86.
L. A. Kalyakin, “Asymptotics of an integral that arises in the theory of perturbations of KdV solitons”, Math. Notes, 50:5 (1991), 1114–1122
1990
87.
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
1989
88.
L. A. Kalyakin, “Long wave asymptotics. Integrable equations as asymptotic limits of non-linear systems”, Russian Math. Surveys, 44:1 (1989), 3–42
1988
89.
L. A. Kalyakin, “Local resonance in a weakly nonlinear problem”, Mat. Zametki, 44:5 (1988), 697–699
90.
L. A. Kalyakin, “Asymptotic transitions from discrete to continuous models”, Theoret. and Math. Phys., 76:3 (1988), 891–894
1989
91.
L. A. Kalyakin, “The matching method in a problem of asymptotic decomposition of a plane wave packet in a dispersive medium”, Dokl. Math., 38:1 (1989), 174–178
1988
92.
L. A. Kalyakin, “Asymptotic decay of a one-dimensional wave packet in a nonlinear dispersive medium”, Math. USSR-Sb., 60:2 (1988), 457–483
1987
93.
L. A. Kalyakin, Differ. Uravn., 23:4 (1987), 696–705
94.
L. A. Kalyakin, “Long-wave asymptotics of the solution to a nonlinear system of equations with small dissipation”, Siberian Math. J., 28:3 (1987), 433–443
1986
95.
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
96.
L. A. Kalyakin, “Long-wave asymptotics of solutions of nonlinear systems of equations with dispersion”, Dokl. Akad. Nauk SSSR, 288:4 (1986), 809–813
1985
97.
L. A. Kalyakin, “Long-wave asymptotics of the solution of the Cauchy problem for a system of equations with nonlinear perturbation”, Dokl. Akad. Nauk SSSR, 283:1 (1985), 18–22
1984
98.
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
1985
99.
L. A. Kalyakin, “Long wave asymptotics of asolution of a hyperbolic system of equations”, Math. USSR-Sb., 52:1 (1985), 91–114
1984
100.
L. A. Kalyakin, Differ. Uravn., 20:2 (1984), 351–353
101.
L. A. Kalyakin, “Construction of the asymptotics of the solution of a degenerate parabolic equation with a small parameter”, Siberian Math. J., 25:3 (1984), 416–423
1983
102.
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
103.
L. A. Kalyakin, Differ. Uravn., 19:11 (1983), 1991–1992
104.
L. A. Kalyakin, Differ. Uravn., 19:4 (1983), 628–644
1982
105.
L. A. Kalyakin, Differ. Uravn., 18:10 (1982), 1724–1738
1979
106.
L. A. Kalyakin, Differ. Uravn., 15:4 (1979), 668–680
107.
L. A. Kalyakin, Differ. Uravn., 15:10 (1979), 1873–1887
1976
108.
L. A. Kalyakin, “On approximate methods of solving nonlinear boundary value problems with a small parameter”, Math. USSR-Sb., 28:4 (1976), 491–500
1974
109.
L. A. Kalyakin, Differ. Uravn., 10:9 (1974), 1684–1691
1972
110.
L. A. Kalyakin, “Approximate solution of certain unstable problems”, Izv. Vyssh. Uchebn. Zaved. Mat., 1972, no. 10, 41–45
111.
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
1971
112.
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
1969
113.
L. A. Kalyakin, “Ritz method for equations with small parameters for higher derivatives”, Math. Notes, 6:1 (1969), 513–516
2024
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