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Depart ment of Differential Equations

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Leonid Anatol'evich Kalyakin

Head of the Department of Differential Equations,
Doctor of Science, Professor

klen@imat.rb.ru

Scientific Interests

  • Application of asymptotic methods for solving nonlinear problems of mathematical physics

  • Autoresonance

Experience

  • 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 four 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.

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Conferences

  • October 3-7, 2005, International Conference on Control and synchronization of dynamical systems, Leon, Mexico
  • International Conference on Complex analysis, Equations of Math. Physics, Computational Mathematics, Yaktykul', Russia, 5-9 December, 2004
  • June 24 - July 3, 2004 Nonlinear Physics: Theory and Experiment.III. Gallipoli - Lecce, Italy.
  • May 16-22, 2004 Int. conference "Differential Equations and Related Topics", Moscow, Russia
  • June, 2003, Kolmogorov and contemporary mathematics. Moscow.
  • June, 2003, Problems of vibrational and acoustical dynamics of constructions and geterogeneous medium. Obninsk, Russia.
  • July 5-12, 2002, Russian seminar"Analytic methods and optimization of process in fluid and gases mechanics" (SAMGOP - 2002), Snezhinsk.
  • June 2002, Nonlinear Evolution Equations and Dynamical Systems (NEEDS '2002), Cadis, Spain.
  • August, 2002, Solitons, Chaos and Turbulence, Chernogolovka, Russia.
  • 5-12 July 2002 Russian school-seminar "Analytical methods and optimization of processes in fluid mechanics" (SAMGOP - 2002), Snezhinsk, Russia
  • 26-30 May 2002 Int. conference "Asymptotics in differential equations", Ufa, Russia
  • 2-9 March 2002 Russian scientific school "Nonlinear waves - 2002", Nizhnii Novgorod, Russia
  • July 2001, Nonlinear Evolution Equations and Dynamical Systems (NEEDS '2001), Cambridge.
  • May, 2001 I.G.Petrovskii conference, Moscow.
  • June 2000, Nonlinear Evolution Equations and Dynamical Systems (NEEDS '2000), Gokova, Turkey.
  • 28 May - 1 June 2000 Int. conference "Complex analysis, differential equations and related problems", Ufa, Russia
  • June 1999, Nonlinear Evolution Equations and Dynamical Systems (NEEDS '99), Crete, Greece.
  • August 1999, Solitons, Chaos and Turbulence, Chernogolovka, Russia.
  • June 22-26, 1999, International conference "Differential and integral equations", Chelyabinsk, Russia
  • 3-8 August 1998 Int. conference "Exactly solvable models in mathematical physics", Chelyabinsk, Russia
  • January, 1998, I.G.Petrovskii conference, Moscow.

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Publications

  • Kalyakin L.A., Asymptotic solution of the problem of threshold effect for the principal resonance equations, Dif. uravn., 2004. (in Russian)
  • Kalyakin L.A., Autoresonance in the dynamical system, Contemporary mathematics and its applications. V. 5. Asymptotic methods of functional analysis. Publishing by Georgian Academy of Sciences, Institute of cybernetics, Tbilisi, 2003. P. 79-108. (in Russian)
  • Kalyakin L.A., Asymptotics for the solutions of the principal resonance equations, Teor. Matem. Fiz., 2003. V. 137, ¹ 1. P. 142-152. (in Russian)
  • Kalyakin L.A., Asymptotic analysis of principal resonance equations and autoresonance phenomenon, Abstracts of "Kolmogorov and contemporary mathematics", Moscow, 2003. P. 54.
  • Kalyakin L.A., Averaging in autoresonance model, Matem. zametki, 2003. V. 73, Is. 3. P. 449-452. (in Russian)
  • Kalyakin L.A., Asymptotics for the solutions of the principal resonance equations at infinity, Dokl. RAS, 2003. V. 388, ¹ 3. P. 305-308. (in Russian)
  • Kalyakin L.A., Autoresonance in the dynamic system, Abstracts of the school-seminar "Analytical methods and optimization of processes in fluid mechanics" (SAMGOP - 2002), Snezhinsk, 2002. P. 30. (in Russian)
  • Kalyakin L.A., Asymptotic analysis of an autoresonance model, V. 9, ¹ 1. 2002. P. 84-95.
  • Kalyakin L.A., Asymptotic solution of the autoresonance problem, Teor. Matem. Fiz., 2002. V. 133, ¹ 3. P. 429-438. (in Russian)
  • Kalyakin L.A., Asymptotic solution of a problem on autoresonance, Abstract in "Differential Equations and Related Topics", Moscow, 2001. P. 176-177.
  • Kalyakin L.A., Asymptotic analysis of a model of the autoresonance, Abstract in "Day on Diffraction'2001", Saint Petersburg, 2001. P. 44-45.
  • Kalyakin L.A., Asymptotic Analysis of the Autoresonance Phenomenon, Abstract in "Progress in nonlinear science", Niznii Novgorod, 2001. P. 242-243.
  • Kalyakin L.A., Averaging of the single-frequency oscillations, Vestnik UGATU, 2001. ¹ 1 (3). P. 40-46. (in Russian)
  • Kalyakin L.A., Weak perturbation of solution with movable singularities, Proc. Steklov Inst. Math. Suppl. 1, 2001. P. S85-S106.
  • Kalyakin L.A., Perturbation of the solutions with movable singularities, Teor. Matem. Fiz., 2001. V. 127, ¹ 3. P. 401-410. (in Russian)
  • Kalyakin L.A., Bulgakova G.T., Hasanov M.M., Studying stability of the gas-liquid filtration, Appl. Mech. Tech. Phys. 2001. V. 64, Is. 2. P. 293-298. (in Russian)
  • Kalyakin L.A., Asymptotic analysis of the autoresonance model, Dokl. RAS, 2001. V. 378, ¹ 5. P. 594-597. (in Russian)
  • Kalyakin L.A., Liouville equation under perturbation , Inverse Problems, 2001. V. 17. P. 879-883.
  • Kalyakin L.A., Singular solution of the Liouville equation under perturbation, Journal of nonlinear mathematical physics, 2001. V. 8, Suppl. P. 156-160.
  • Kalyakin L.A., Bulgakova G.T., Hasanov M.M., Studying stability of the gas-liquid filtration, Appl. Mech. Tech. Phys. 2000. V. 41, Is. 6. P. 78-85. (in Russian)
  • Kalyakin L.A., Asymptotic decay of the solution of the perturbed Liouville equation, Matem. zametki, 2000. V. 68, ¹ 2. P. 195-208. (in Russian)
  • Kalyakin L.A., Perturbation of the movable singularities, Proceedings of the Int. conference "Complex analysis, differential equations and related problems", Ufa, 2000. P. 84-88. (in Russian)
  • Kalyakin L.A., Perturbation of smooth solutions of the Liouville equation, in "Actual Problems of Mathematics. Math. Methods in Natural Sciences", Ufa: USATU, 1999. P. 136-149. (in Russian)
  • Kalyakin L.A., Perturbation of singular solution of the Liouville equation, Teor. Matem. Fiz., 1999. V. 118, ¹ 3. P. 390-396. (in Russian)
  • Kalyakin L.A., Shakir'yanov M.M., Asymptotics for the solution of the Cauchy problem for two-dimensional homogeneous wave equation, Dif. uravn. 1999. V. 35, ¹ 9. (in Russian)
  • Kalyakin L.A., Shakir'yanov M.M., Asymptotics of the Poisson integral at a large time, in "Problems of Mathematics and Control Theory", Ufa, 1998. P. 58-65. (in Russian)
  • Glebov S.G., Kalyakin L.A., Local resonances in nonlinear waves, in "Problems of Mathematics and Control Theory", Ufa, 1998. P. 54-57. (in Russian)
  • Kalyakin L.A., Weak interaction of the perturbed Korteweg-de Vries solitons, Fund. Appl. Math. 1998. V. 4, ¹ 3. P. 3-27. (in Russian)
  • Kalyakin L.A., Perturbation of the degenerated plane wave in the system of the Navier-Stokes equations, Dokl. RAS, 1998. V. 360, ¹ 3. P. 328-330. (in Russian)
  • Kalyakin L.A., Singular solutions of the linearized Liouville equation, Uspehi matem. nauk, 1998. V. 53, Is. 4. P. 179. (in Russian)
  • Kalyakin L.A., Asymptotic Well-Posedness for the Problem of Soliton Perturbation, Russian Journal of Math. Physics, 1997. V. 5, ¹ 4. P. 447-458.
  • Kalyakin L.A., Lazarev V.A., Perturbation of the two-soliton solution of the KdV equation, Teor. Matem. Fiz., 1997. V. 112, ¹ 1. P. 92-102. (in Russian)
  • Kalyakin L.A, Maslennikov S.I., Method of asymptotic approximations in mathematical modelling of the chemical kinetics problems, Math. Modelling, 1997. V. 9, ¹ 8. P. 60-69. (in Russian)
  • Il'in A.M., Maslennikov S.I., Kalyakin L.A., The matching method for asymptotic solution in chemical physics problems, Advances in Chemical Physics, 1997. V. 47. P. 1-46.
  • Kalyakin L.A., Perturbation of the degenerated plane simple wave in hyperbolic system of equations, in "Complex analysis, differential equations, numerical methods and applications. III. Differential equations". Ufa, 1996. P. 84-92. (in Russian)
  • Kalyakin L.A., Correctness of the problem of soliton perturbation, Uspehi matem. nauk, 1996. V. 51, Is. 5. P. 145. (in Russian)
  • Kalyakin L.A., Shakir'yanov M.M., Correctness of the Goursat-Cauchy problem for the Davey-Stewartson system, Dokl. RAS, 1996. V. 346, ¹ 4. P. 445-447. (in Russian)
  • Kalyakin L.A., Weak interaction of the KdV soliton under perturbation, Physica D, 1995. V. 87. P. 193-200.
  • Kalyakin L.A., Asymptotic correctness of the problem of the Korteweg-de Vries soliton's perturbation, in "Asymptotics and symmetries in nonlinear dynamic systems", Ufa, 1995. P. 38-52. (in Russian)
  • Kalyakin L.A., To the problem on the first correction in the theory of soliton's perturbation, Matem. sb. 1995. V. 186, ¹ 7. P. 51-76. (in Russian)
  • Kalyakin L.A., Asymptotics of the first correction in the perturbation of N-soliton solution of the KdV equation, Matem. zametki, 1995. V. 58, ¹ 2. P. 204-217. (in Russian)
  • Kalyakin L.A., Shakir'yanov M.M., Solvability of the boundary-value problems in the systems of the Davey-Stewartson type equations, Uspehi matem. nauk, 1995. V. 50, Is. 4. P. 75-76. (in Russian)
  • Kalyakin L.A., Il'in A.M., Perturbation of the finite-soliton solutions of the Korteweg-de Vries equation, Dokl. RAS, 1994. V. 334, ¹ 5. P. 595-598. (in Russian)
  • Glebov S.G., Kalyakin L.A., On the solvability of nonlinear equation of Shr\"odinger type in the class of rapidly oscillating functions, Matem. zametki. V. 56, 1994. P. 32-40. (in Russian)
  • Kalyakin L.A., On the first correction in the theory of soliton's perturbation, Matem. sb. 1994. V. 49, ¹ 4. P. 104-105. (in Russian)
  • Kalyakin L.A., Maslennikov S.I., Komissarov V.D., , The method of asymptotic approximation as applied o analysing the mechanism of inhibited liquid-phase oxidation, International Journal Chemical Kinetics, 1993. V. 25. P. 681-700.
  • Kalyakin L.A., Asymptotics of the first correction in the theory of soliton's perturbation, Uspehi matem. nauk, 1993. V. 48, Is. 4. P. 221. (in Russian)
  • Kalyakin L.A., The first order corrections and justification of soliton perturbation, Preprint Institute of Mathematics RAS, 1992. 13 p.
  • Kalyakin L.A., Squares of the Jost functions as a solution of linearized equation, in "Asymptotic methods for the solution of the differential equations". Ufa, 1992. P. 40-60. (in Russian)
  • Kalyakin L.A., Perturbation of the Korteweg-de Vries soliton, Teor. Matem. Fiz., 1992. V. 92, ¹ 1. P. 62-76. (in Russian)
  • Kalyakin L.A., Asymptotics of one integral appearing in the theory on perturbation of KdV solitons, Matem. zametki, 1991. V. 50, ¹ 5. P. 32-42. (in Russian)
  • Kalyakin L.A., Matching method in the problem of long-wave modulation of nonlinear plane waves with a dispersion, Proc. MMO, 1990. V. 53. P. 3-41. (in Russian)
  • Kalyakin L.A., The nonlinear Schrodinger equation with variable coefficients as an asymptotical limit of nonlinear system with strong dispersion, Preprint, Dipartimento di fisica Universita di Roma "La Sapienza", 1989. ¹ 648.
  • Kalyakin L.A., VKB method in weakly nonlinear problem with the local resonance, in , Ufa, BSC, 1989. P. 56-69. (in Russian)
  • Kalyakin L.A., Long-wave asymptotics. Integrable equations as asymptotic limit of nonlinear systems, Uspehi matem. nauk, 1989. V. 44, Is. 1. (in Russian)
  • Kalyakin L.A., Local resonance in the weakly nonlinear problem, Matem. zametki, 1988. V. 44, ¹ 5. P. 697-699. (in Russian)
  • Kalyakin L.A., Long-wave asymptotics for the solutions of multi-dimensional Boussinesq equation, in , Ufa, BSC, 1988. P. 28-44. (in Russian)
  • Kalyakin L.A., On the asymptotic transfer from discrete to continuous models, Teor. Matem. Fiz., 1988. V. 76, ¹ 3. P. 323-327. (in Russian)
  • Kalyakin L.A., Maslennikov S.I., Komissarov V.D., Analysis of the mechanism of the liquid-phase inhibited oxidation by the asymptotic approximations method , Preprint, BNC, 27 p. (in Russian)
  • Kalyakin L.A., Maslennikov S.I., Komissarov V.D., Analysis of the mechanism of the liquid-phase inhibited oxidation by the asymptotic approximations method , deposited in VINITI ¹ 4998-Â87. (in Russian)
  • Kalyakin L.A., Matching method in the problem of asymptotic decay of the plane wave packet in a dispersive medium, Dokl. AN SSSR, 1988. V. 301, ¹ 5. P. 1048-1052. (in Russian)
  • Kalyakin L.A., Long-wave asymptotics in nonlinear systems of equations with a dispersion, Uspehi matem. nauk, 1987. V. 42, Is. 4. (in Russian)
  • Kalyakin L.A., Long-wave asymptotics for the solution of nonlinear system of equations with a small dissipation, Sib. matem. J. 1987. V. 28, ¹ 3. P. 101-114. (in Russian)
  • Kalyakin L.A., Long-wave asymptotics for the solution of nonlinear system of equations with a small dispersion, Dif. uravn. 1987. V. 23, ¹ 4. P. 696-705. (in Russian)
  • Kalyakin L.A., Asymptotic decay of the one-dimensional wave packet in nonlinear dispersive medium, Matem. sb. 1987. V. 132, ¹ 4. P. 470-495. (in Russian)
  • Kalyakin L.A., Long-wave asymptotics in nonlinear problems, Abstracts of XI school on the theory of operators, 1986. (in Russian)
  • Kalyakin L.A., Long-wave asymptotics for the solutions of nonlinear system of equations with a dispersion, Dokl. AN SSSR, 1986. V. 288, ¹ 4. P. 809-813. (in Russian)
  • Kalyakin L.A., Long-wave asymptotics for the solutions of nonlinear system of equations, Preprint, BFAN, 1985, 35 p. (in Russian)
  • Kalyakin L.A., Nonlinear Schr\"odinger equation as an asymptotic limit of the nonlinear system of equations with a dispersion, Uspehi matem. nauk, 1985. V. 40, Is. 5. (in Russian)
  • Kalyakin L.A., Long-wave asymptotics for the solution of the Cauchy problem for the system of equations with nonlinear perturbation, Dokl. AN SSSR, 1985. V. 283, ¹ 1. P. 18-22. (in Russian)
  • Kalyakin L.A., Asymptotic integration of the perturbed hyperbolic system of equations in the class of conditionally periodic functions, Proc. MMO, 1986. V. 49. P. 56-70. (in Russian)
  • Kalyakin L.A., Long-wave asymptotics in hyperbolic systems, Uspehi matem. nauk, 1983. V. 38, Is. 6. (in Russian)
  • Kalyakin L.A., Long-wave asymptotics for the solution of hyperbolic system of equations, Matem. sb. 1984. V. 124, ¹ 1. P. 96-120. (in Russian)
  • Kalyakin L.A., Asymptotics for the solution of hyperbolic system of equations with nonlinear perturbation, Uspehi matem. nauk, 1984. V. 39, Is. 5. P. 243-244. (in Russian)
  • Kalyakin L.A., Asymptotic decay in simple waves of the solution of the perturbed hyperbolic equations system, in , Sverdlovsk, UNC, 1984. (in Russian)
  • Kalyakin L.A., Asymptotic expansion for the solution of the degenerating parabolic equation with a small parameter, Sib. matem. J. 1984. V. 25, ¹ 3. P. 95-102. (in Russian)
  • Kalyakin L.A., Asymptotic expansion for the solution of the degenerating parabolic equation with a small parameter, Uspehi matem. nauk, 1983. V. 38, Is. 1. P. 169-170. (in Russian)
  • Kalyakin L.A., Asymptotic decay in simple waves of the solution of the perturbed hyperbolic system, Uspehi matem. nauk, 1982. V. 37, Is. 4. (in Russian)
  • Kalyakin L.A., Asimptotic integration of hyperbolic equations with weakly nonlinear perturbation, Dif. uravn. 1984. V. 20, ¹ 2. P. 251-253. Deposited in VINITI ¹ 688-83. (in Russian)
  • Kalyakin L.A., Constructing asymptotic expansion for the solution of hyperbolic equation with weakly nonlinear perturbation, Dif. uravn. 1983. V. 19, ¹ 11. P. 1991-1992. Deposited in VINITI ¹ 689-83. (in Russian)
  • Kalyakin L.A., Asymptotics for the solution of the system of two linear MGD equations with a singular perturbation. 1. Complete asymptotic expansion, Dif. uravn. 1983. V. 19, ¹ 4. P. 628-644. (in Russian)
  • Kalyakin L.A., Asymptotics for the solution of the system of two linear MGD equations with a singular perturbation. 1. Standard problem in the elliptic layer, Dif. uravn. 1982. V. 18, ¹ 10. P. 1724-1738. (in Russian)
  • Kalyakin L.A., Elliptic perturbation of the dynamic system with a saddle point on the domain boundary, in , Ufa, BFAN, 1980. P. 3-33. (in Russian)
  • Kalyakin L.A., Methods of matching asymptotic expansions in some linear MGD problems with a singular perturbation, in , Sverdlovsk, UNC, 1980. P. 16-43. (in Russian)
  • Kalyakin L.A., Asymptotics for the solution of the elliptic problem with a singular perturbation in the case of limit operator with a saddle point, in , Sverdlovsk, UNC, 1979. Is. 28. P. 15-39. (in Russian)
  • Kalyakin L.A., Constructing asymptotics of the solution of one MGD problem with a small parameter. 1. Straight-line flow in the canal with a rectangular projection, Dif. uravn. 1979. V. 15, ¹ 10. P. 1873-1887. (in Russian)
  • Kalyakin L.A., Constructing asymptotics of the solution of one MGD problem with a small parameter. 1. Straight-line flow in the rectangular canal, Dif. uravn. 1979. V. 15, ¹ 4. P. 668-680. (in Russian)
  • Kalyakin L.A., Asymptotics for the solution of one system of elliptic equations with a small parameter, deposited in VINITI ¹ 2388-78, ¹ 2389-78, ¹ 3100-78. 1978. (in Russian)
  • Kalyakin L.A., Variational inequalities with a small parameter and the approximate methods of their solving, Proc. of the conference on ill-posed problems, Frunze, 1979. (in Russian)
  • Kalyakin L.A., On the variational inequalities with a small parameter, Abstracts of the School on the theory of operators, ¹2, Dif. equations. Novosibirsk, 1977. (in Russian)
  • Kalyakin L.A., Approximation of the nonlinear nonstationary problems with a small parameter, Banach Center Publication. Warsawa, 1977. V. 3. P. 83-88.
  • Kalyakin L.A., On the variational inequalities with a small parameter, in , Sverdlovsk, UNC, 1976. (in Russian)
  • Kalyakin L.A., On the approximate methods of solving nonlinear problems with a small parameter, Matem. sb. 1976. V. 99, ¹ 4. P. 548-558. (in Russian)
  • Kalyakin L.A., L'approximation des problemes nonlineares avec petit parametre , Comptes Rendus Ac. Sc. de Paris A, 1975. ¹ 281. P. 625-628.
  • Il'in A.M., Yemel'yanov K.V., Shishkin G.I., Kalyakin L.A., Solution of differential equations with a small parameter, Proc. of the seminar on the numerical methods, Novosibirsk, 1975. (in Russian)
  • Kalyakin L.A., On the number of coordinate functions in the projection methods of solving unstable problems, in , Sverdlovsk, UNC, 1975. P. 53-66. (in Russian)
  • Kalyakin L.A., On the first boundary-value problem for elliptic equations in unbounded domain, Dif. uravn. 1974. V. 10, ¹ 9. P. 1684-1691. (in Russian)
  • Kalyakin L.A., Approximate solution of some unstable problems, Izvestiya VUZov, ser. Matem. 1972. ¹ 10. P. 41-45. (in Russian)
  • Kalyakin L.A., On approximate solution of ill-posed problems in normalized spaces, J. vych. matem. i matem. fiz., 1972. V. 12, ¹ 5. P. 1168-1181. (in Russian)
  • Kalyakin L.A., Galerkin's method for equations with a small parameter, Matem. sb., 1971. V. 85, ¹ 4. P. 527-537. (in Russian)
  • Kalyakin L.A., Ritz' method for equations with a small parameter, Matem. zametki, 1969. V. 6. Is. 1. P. 91-96. (in Russian)

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L.A. Kalyakin