Oleg Mikhailovich Kiselev

Leading Researcher,
Doctor of Science, Professor

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Scientific Interests

• Nonlinear equations of mathematical physics, solitons, asymptotics of the solutions on long times

• Asymptotics for the solutions of nonlinear ordinary differential equations, perturbation of periodic solutions, behavior of the solutions near homoclinic trajectories

• Soliton generation

• Separatrices and turning towards chaos in solutions of ordinary differential equations

Experience

• 1988 Mechanical Engineer diploma with honours on aviation engines, Aviation Engines Faculty, Ufa Aviation Institute. Degree work - "Working out the universal model of GTE".
• 1988-1993 Probationer, post-graduate student, junior researcher, Institute of Mathematics, Ufa Scientific Center of RAS.
• 1993 PhD, thesis "Asymptotic behaviour of solution for Cauchy problem for semi-linear perturbed hyperbolic equations".
• 1993-2000 Researcher, Senior Researcher, Institute of Mathematics, Ufa Scientific Center of RAS.
• Senior Researcher diploma, Senior Researcher, Institute of Mathematics, Ufa Scientific Center of RAS.
• 2002 Doctor's degree, thesis "Multi-dimensional nonlinear integrable equations: asymptotic behaviour of solutions and perturbations".

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Conferences

• Conference on Nonlinear Equations and Complex Analysis (Bannoe - Yaktykul', December 17-21, 2007, Russia)
• International Conference Dynamical methods and mathematical modelling (September 18-22, 2007, Valladolid, Spain).
• Session of the Council of Nonlinear Dynamics (December 24-25, 2007, Moscow, Russia).
• International Conference Analytical Methods of Celestian Mechanics (July 8-12, 2007, Saint-Petersburg, Russia).
• International Conference on Differential Equations and Dynamical Systems (July 10-15, 2006, Suzdal, Russia).
• Session of the Council of Nonlinear Dynamics (December 25-26, 2006, Moscow, Russia).
• Conference on Complex Analysis and Differential Equations (December 4-8, 2006, Bannoe, Russia).
• International Conference " Nonlinear Physics. Theory and Experiment. IV " (June 22 - July 1, 2006, Gallipoli (Lecce), Italy).
• Soliton generation by local resonance interaction
• International Conference on Complex analysis, Equations of Math. Physics, Computational Mathematics (Yaktykul', Russia, 5-9 December, 2004
• International Conference on Asymptotics in Differential Equations, Ufa, Russia, Ufa, Russia, May 26-30, 2002.
• Asymptotic behaviuor of a solution for Kadomtsev-Petviashvili-2 equation
  Akhiezer Centenary International Conference " "The Theory of Functions and Mathematical Physics"" (12-17 August, 2001, Kharkiv, Ukraine).
• Asymptotic description of separatrix crossing near a saddle-center point
  Andronov Centenary Conference "Progress in Nonlineear Science" (2-6 July, 2001, Nizhnii Novgorod).
• Asymptotic solution of primary resonance equation in bifurcation layer
  Petrovskii Centenary Conference " "Differential equations and related topics"" (22-27 May, 2001, Moscow, Russia).
• (2+1)-dimensional integrable equations: asymptotics and perturbations
  This review lecture was presented at:
  - seminar of Acad. A.M. Il'in. Institute of Mathematics and Mechanics, Ekaterinburg, March 28, 2000 - seminar of Acad. V.A.Marchenko and Prof. E.Ya. Khruslov. Institute for Low Temperature, Kharkov, Ukraine, April 19, 2000 - seminar of Prof. A.B. Shabat. Landau Institute of Theoretical Physics, Cernogolovka, April 21, 2000 - seminar of Acad. V.P.Maslov and Prof. S.Yu.Dobrokhotov. Institute Problems of Mechanics, Moscow, May 24, 2000 - seminar of Prof. V.M. Babich. SPb. Branch of Steklov Mathematical Institute, S.-Petersburg, May 26, 2000 - seminar of Prof. V.V. Pukhnachev. Institute of Hydrodynamics, Novosibirsk, December 13, 2000 - seminar of Prof. T.I. Zelenyak. Sobolev Institute of Mathematics, Novosibirsk, Desember 14, 2000
• (2+1)-dimensional solitons under perturbations (PDF-file, 453 kB)
  conference "Nonlinear Evolution Equations and Dynamical Systems" (June 30-July 7, 2000, Gokova, Turkey).
• Hard loss of stability in Painleve-2 equation (PDF-file, 155 kB)
  conference "Day on Diffraction" (May 29-June 1, 2000, Saint-Petersburg, Russia).
• Asymptotic approach for rigid condition for rise of oscillations in solution for the Painleve'-2 equation.
  conference "Solitons, Collapses and Turbulence: Achievements, Developments and Perspectives" (Chernogolovka, Russia, 3-10 August, 1999).
• On the lump instability of the Davey-Stewartson II equation.
  conference "Exactly Solvable Models in Math Physics" (Chelyabinsk, Russia, 3-8 August 1998).

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Publications

• S.G. Glebov, O.M. Kiselev, V.A. Lazarev The autoresonance threshold in a system of weakly coupled oscillators. Proceedings of the Steklov Institute of Mathematics. Suppl. 1, 2007, S111-123
• S.G. Glebov, O.M. Kiselev, V.A. Lazarev The autoresonance threshold into a system of weakly coupled oscillators.arxiv.org/abs/0707.2311
• O.M. Kiselev, S.G. Glebov The capture into parametric autoresonance. Nonlinear Dynamics, v48, n1-2, 2007, pp.217-230
• O.M. Kiselev Asymptotics of solutions of higher-dimensional integrable equations and their perturbations. Journal of Mathematical Sciences, v138, n6, 2006, pp. 6067-6230.
• S.G. Glebov, O.M. Kiselev. Resonant excitation of waves in KDV equation. Materialen zum wissenschaftlichen Seminar der Stipendiaten des "Michail Lomonosov" programms 2005/06. DAAD - Min.fur Bild. und Forschung der RF, Moskau, 24-25 April, 2006, pp.38-41.
• N.K. Gorbatova, O.M. Kiselev, S.G. Glebov. Resonant excitation of nonlinear waves. AIP Conference Proceedings, v.834, 2006, pp.196-205.
• Gorbatova N., Kiselev O., Glebov S. Finite amplitude waves under a small resonant driving. arXiv:force. nlin.PS/0512049, 20 Dec 2005.
• Kiselev O.M., Glebov S.G. The capture into parametric resonance. arXiv:math-ph/0511017v1, 4Nov 2005.
• Glebov S. G. and Kiselev O.M. The forced KdV equation and passage through the resonance. Preprint 2005/21 ISSN 1437-739X, Institut fur Mathematik, Uni Potsdam, 2005
• S.G.Glebov, O.M. Kiselev. The slowly passage through the resonances and wave packets with the different carriers. Dynamics of Partial Differential Equations Vol. 2, No. 3 2005, p.261 (см. также ArXiv: math-ph # 0503019.)
• S.G. Glebov, O.M. Kiselev. The stimulated scattering of solitons on a resonance. Journal of Nonlinear Mathematical Physics, 2005, v.12, n3, p.330-341.
• S.G.Glebov, O.M. Kiselev, V.A. Lazarev. Slow passage through resonance for a weakly nonlinear dispersive wave. SIAM Journal of Applied Mathematics, 2005, vol.65,n6, pp.2158-2177.
• Kiselev O.M. Asymptotics of solutions for the multidimensional integrable equations and its perturbations. //Contemporary mathematics. Fundamental trend., 2004, v.11, p.3-149.
• Kiselev O.M., Glebov S.G., Lazarev V.A. Resonant pumping in nonlinear Klein-Gordon equation and solitary packets of waves. ArXiv:math-ph/0410041
• Kiselev O.M., Glebov S.G. Scattering of solitons on resonance. Asymptotics and numeric simulations. // arXiv:nlin.PS/0410024 v1 18 Oct 2004, p.1-14.
• Kiselev O.M., Glebov S.G. Scattering of solitons on resonance. //ArXiv: math-ph # 0403038.
• O.M. Kiselev, Multidimesional nonlinear equations: asymptotics of solutions and perturbations. Contemporary mathematics and its applications. V. 5. Asymptotic methods of functional analysis. Publishing by Georgian Academy of Sciences, Institute of cybernetics, Tbilisi, 2003. P. 109-134. (in Russian)
• S.G.Glebov, V.A.Lazarev, O.M. Kiselev. Generation of solitary packets of waves by resonance. Proceedings of International seminar "Day on Diffraction-2003", SPb. Russia. pp.46-51.
• O.M. Kiselev, S.G.Glebov.An asymptotic solution slowly crossing the separatrix near a saddle-center bifurcation point. Nonlinearity, 2003, v.16, pp.327-362.
• S.G.Glebov, O.M. Kiselev, V.A.Lazarev. Birth of solitons during passage through local resonance. Proceedings of the Steklov Institute of Mathematics. Suppl., 2003, issue 1, S84-S90.
• O.M. Kiselev, S.G.Glebov. Asymptotic description of separatrix crossing near a saddle-center point. Progress in nonlinear science. Proceedings of International conference dedicated to the 100th anniversary of A.A. Andronov. Vol.1, Mathematical problem of nonlinear dynamics, Nizhny Novgorod, 2002, pp.269-274
• R.R. Gadyl'shin, O.M.Kiselev. Perturbation of the soliton for Davey-Stewartson II equation. Matem. Fiz., Analiz, Geom., 2002, V. 9, N 2. P. 272-280.
• O.M. Kiselev, Krylov-Bogolyubov ansatz for nonlinear nonautonomous second order equation. Review. 22 pages. (in Russian)
• S.G. Glebov, O.M.Kiselev. Applicability of the WKB method in the perturbation problem for the equation of Principal resonance. Russian J. of Math. Phys., v.9, n1, 2002, pp.60-83
• O.M. Kiselev, Asymptotics of a solution of the Kadomtsev-Petviashvili-2 equation. Proceedings of the Steklov Institute of Mathematics. Suppl. 1, 2001. (in Russian)
• O.M.Kiselev, S.G.Glebov. Asymptotic decsription of nonlinear resonance.
  ArXiv: math.DS # 0105011.

• O.M.Kiselev. Hard Loss of Stability in Painleve-2 Equation.
  Journal of Nonlinear Mathematical Physics, 2001, v.8, n1, p.65-95.

• O.M.Kiselev. Dromion Perturbation for the Davey-Stewartson-1 Equations.
  Journal of Nonlinear Mathematical Physics, 2000, v.7, n4, p.411-422.

• S.G. Glebov, O.M. Kiselev, Asymptotics of a rigid generation of natural oscillations I.
  Proceedings of the Int. conference "Complex analysis, differential equations and related problems", Part I. Ufa, 2000. P. 49-52. (in Russian)
• O.M. Kiselev, S.G. Glebov, Asymptotics of a rigid generation of natural oscillations II.
  Proceedings of the Int. conference "Complex analysis, differential equations and related problems", Part I. Ufa, 2000. P. 95-97. (in Russian)
• O.M. Kiselev, Perturbation of a solitary wave of the nonlinear Klein-Gordon equation.
  Siberian Mathematical Journal, 2000, V. 41, N 2. P. 345-358. (in Russian)
• O.M.Kiselev. Asymptotic behaviour of a solution for Kadomtsev-Petviashvili-2 equation.
  PBB math-ph # 0003014.
• O.M.Kiselev. Asymptotics of soliton solution for the perturbed Davey-Stewartson-I equations.
  PBB math-ph # 9909028.
• R.R.Gadyl'shin, O.M. Kiselev, Structural instability of soliton for the Davey-Stewartson II equation II.
  Teor. Matem. Fiz., 1999, V. 118, N 3. P. 354-361. (in Russian)
• O.M. Kiselev, Asymptotic behavior of the solution for two-dimensional Dirac system with rapidly oscillating coefficients.
  Matem. sb., 1999, V. 190, N 2. P. 71-92. (in Russian)
• O.M. Kiselev. Asymptotic approach for the rigid condition of appearance of the oscillations in the solution of the Painleve-2 equation.
  PBB solv-int # 9902007.
• O.M. Kiselev, B.I. Suleimanov. The solution of the Painleve equations as special functions of catastrophes, defined by a rejection in these equations of terms with derivative.
  PBB solv-int # 9902004.
• O.M. Kiselev, The basic functions associated with a two-dimensional Dirac system.
  Funk. anal. pril., 1998, V. 32, N 1. P. 72-76. (in Russian)
• R.R.Gadyl'shin, O.M.Kiselev. Asymptotics of perturbed soliton solution for the Davey-Stewartson II equation.
  PBB solv-int # 9801014.
• R.R.Gadyl'shin, O.M.Kiselev. On lump instability of the Davey-Stewartson II equation.
  PBB solv-int # 9804001.
• O.M.Kiselev. Perturbation theory for the Dirac equation in the two-dimensional space.
  Journal of Math. Phys., 1998, v.39, n4, p.2333-2345.
• O.M. Kiselev, Asymptotic behavior of the solution for the Cauchy problem of the Davey-Stewartson I equation.
  Teor. Matem. Fiz., 1998, V. 114, N 1. P. 104-114. (in Russian)
• O.M. Kiselev, Asymptotic behavior of the nonsoliton solution of the Davey-Stewartson II equation.
  Dif. uravn., 1997, V. 33, N 6. P. 812-819. (in Russian)
• O.M. Kiselev, The Fourier method for the linearized Davey-Stewartson I equation.
  in "Complex analysis, differential equations, numerical methods and applications. III. Differential equations. Ufa, 1996. P. 93-97. (in Russian)
  PBB solv-int # 9701014 (in English).
• O.M.Kiselev. The interaction of a kink with a breather of small amplitude in the phi^4-model.
  Russian Journ. of Math.Phys., 1997, v.5, n1, p.29-46.
• O.M. Kiselev, The basic functions associated with a two-dimensional Dirac system.
  Uspehi matem. nauk, 1996, V. 51, N 5. P. 230. (in Russian)
• R.R.Gadyl'shin, O.M. Kiselev, On solitonless structure of the perturbed soliton solution for the Davey-Stewartson equation.
  Teor. Matem. Fiz., 1996, V. 106, N 2. P. 167-173. (in Russian)
• O.M. Kiselev, Asymptotics of the Cauchy problem solution for the semilinear hyperbolic system with the strong dispersion.
  in "Asymptotics and symmetries in nonlinear dynamical systems". Ufa, 1996. P. 52-70. (in Russian)
• O.M. Kiselev, Asymptotics of a multiple Cauchy integral with rapidly oscillating exponential.
  Matem. zametki, 1995, V. 58, N 2. P. 833-840. (in Russian)
• O.M. Kiselev, Solution of Goursat problem for the Maxwell - Bloch system.
  Teor. Matem. Fiz., 1994, V. 98. P. 20-26. (in Russian)
• O.M. Kiselev, The formal solution of the Goursat problem for the Sine-Gordon equation.
  in "Integrability in dynamical systems". Ufa, 1994. P. 17-26. (in Russian)
• O.M. Kiselev, Kink asymptotics of the perturbed Sine-Gordon equation.
  Teor. Matem. Fiz., 1992, V. 93, N 1. P. 1106-1111. (in Russian)
• O.M. Kiselev, On the asymptotics of the iterated Fourier type integral.
  in "Asymptotic methods for the solution of the differential equations". Ufa, 1992. P. 61-73. (in Russian)
• O.M. Kiselev, The formal asymptotics of the soliton solution for the Sine-Gordon equation.
  in "Asymptotic solutions of the problems of the mathematical physics". Ufa, 1990. P. 50-62. (in Russian)
• O.M. Kiselev, Asymptotic behavior of the Cauchy problem for the reduced Maxwell-Bloch system.
  in "Asymptotic methods for the solutions of the mathematical physics problems". Ufa, 1989. P. 70-81. (in Russian)
• O.M. Kiselev, Asymptotic behavior of the Cauchy problem for the perturbed Klein-Fock-Gordon equation.
  Zap. Nauch. Semin.LOMI, 1987, V. 165. P. 115-121. (in Russian)

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