Oleg Kiselev

	Kiselev Oleg Michailovich, doctor of phys.-math. sciences, leading reseacher in Institute of Mathematics of Russian Academy of Sciences (Ufa). The field of scientific interests is asymptotic behavior of solutions for nonlinear differential equations, solitons, selforganization and chaos.
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	Courses of studies

	Monster Zoo or Introduction into special functions (in Russian) Introduction into the theory of nonlinear oscillations (in Russian) Ordinary differential equations (in Russian) Partial differential equations (in Russian) Methods of Mathematical Physics (in Russian) Hamiltonian mechanics (in Russian)
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	Lectures

	Scattering of autoresonance trajectories upon a separatrix This lecture was presented at: Asymptotic methods for theory of boundary problems (June 7-12, 2011, lake Elovoe, Schebarkul, Russia). the Session of the Council of Nonlinear Dynamics (December 26-27, 2011, Moscow, Russia). Scattering on separatrix This lecture was presented at: Conference on Nonlinear Equations and Complex Analysis (Bannoe - Yaktykul', December 13-17, 2010) Autoresonance in dissipative system (PDF-file, see in presentation mode) This lecture was presented at: Conference on Nonlinear Equations and Complex Analysis (Bannoe - Yaktykul', December 14-18, 2009) the Session of the Council of Nonlinear Dynamics (December 21-21, 2009, Moscow, Russia). Slow passage through parametric resonance for a weakly nonlinear dispersive wave (PDF-file, see in presentation mode) This lecture was presented at: - the International Conference " Nonlinear Physics. Theory and Experiment. V " (June 12-21, 2008, Gallipoli (Lecce), Italy). Oscillations on Cantor manifolds This lecture was presented at: Conference on Nonlinear Equations and Complex Analysis (Bannoe - Yaktykul', December 17-21, 2007) The autoresonance threshold in a system of weakly coupled oscillators (PDF-file) This lecture was presented at: the International Conference Dynamical methods and mathematical modelling (September 18-22, 2007, Valladolid, Spain). the Session of the Council of Nonlinear Dynamics (December 24-25, 2007, Moscow, Russia). The capture into parametric autoresonance (PDF-file) This lecture was presented at: the International Conference Analytical Methods of Celestian Mechanics (July 8-12, 2007, Saint-Petersburg, Russia). the International Conference on Differential Equations and Dynamical Systems (July 10-15, 2006, Suzdal, Russia). Slow passage through resonance for a weakly nonlinear dispersive wave (PDF-file) This lecture was presented at: - the Session of the Council of Nonlinear Dynamics (December 25-26, 2006, Moscow, Russia). - the Conference on Complex Analysis and Differential Equations (December 4-8, 2006, Bannoe, Russia). - the International Conference " Nonlinear Physics. Theory and Experiment. IV " (June 22 - July 1, 2006, Gallipoli (Lecce), Italy). Soliton generation by local resonance interaction (PDF-file) This lecture was presented at the International Conference " Mathematical modelling of wave phenomena" (August 14-19, 2005, Vaxjo, Sweden). Asymptotic behaviuor of a solution for Kadomtsev-Petviashvili-2 equation (PDF-file) This lecture was presented at the Akhiezer Centenary International Conference "The Theory of Functions and Mathematical Physics" (August 12-17, 2001, Kharkov, Ukraine). Asymptotic description of separatrix crossing near a saddle-center point This lecture was presented at the International Conference "Progress in Nonlineear Science"Dedicated to the 100th anniversary of A.A.Andronov (July 2-6, 2001, Nizhni-Novgorod, Russia). Asymptotic solution of primary resonance equation in bifurcation layer This lecture was presented at the Petrovskii Centenary Conference "Differential equations and related topics" (May 22-27, 2001, Moscow, Russia). (2+1)-dimensional integrable equations: asymptotics and perturbations (in Russian) 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) This lecture was presented at the International 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) This lecture was presented at the International Conference "Day on Diffraction" (May 29-June 1, 2000, St.Petersburg, Russia). Asymptotic approach for rigid condition for rise of oscillations in solution for the Painleve'-2 equation This poster was presented at the International Conference "Solitons, Collapses and Turbulence: Achievements, Developments and Perspectives" (August 3-10, 1999, Chernogolovka, Russia). On the lump instability of the Davey-Stewartson II equation This lecture was presented at the International Conference "Exactly Solvable Models in Math Physics" (August, 3-8, 1998, Chelyabinsk, Russia).
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	Papers

	Oleg Kiselev, and Nikolai Tarkhanov Scattering of autoresonance trajectories upon a separatrix Prepint Institut fur Mathematik Universitat Potsdam, November 10, 2011. Sergei Glebov, Oleg Kiselev, and Nikolai Tarkhanov Forced nonlinear resonance in a system of coupled oscillators Chaos 21, 023109 (2011); doi:10.1063/1.3578047 (7 pages) Sergei Glebov, Oleg Kiselev, and Nikolai Tarkhanov Autoresonance in a dissipative system J. Phys. A: Math. Theor. 43 (2010) 215203 Sergei Glebov, Oleg Kiselev, and Nikolai Tarkhanov Weakly Nonlinear Dispersive Waves under Parametric Resonance Perturbation. Studies in Applied Mathematics, 10.1111/j.1467-9590.2009.00460.x O. Kiselev, I. Shestakov Asymptotics of solutions to the Laplace–Beltrami equation on a rotation surface with a cusp. Journal of Mathematical Analysis and Applications, Volume 362, Issue 2, 15 February 2010, Pages 393-400 Sergei Glebov, Oleg Kiselev, Nikolai Tarkhanov Autoresonance in a Dissipative System. http://arxiv.org/abs/0912.0133 O.M. Kiselev Oscillations near separatrix for perturbed Duffing equation. http://arxiv.org/abs/0903.4523 Oleg Kiselev, Sergei Glebov Autoresonant germ in dissipative system. http://arxiv.org/abs/0902.4595 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. N.K. Gorbatova, O.M. Kiselev, S.G. Glebov. Finite amplitude waves under a small resonant driving force ArXiv: nlin.PS # 0512049 O.M. Kiselev, S.G. Glebov. The capture into parametric autoresonance ArXiv: math-ph # 0511017 S.G. Glebov and O.M. Kiselev. 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. (PDF-file) (see also 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. O.M. Kiselev. Asymptotics of solutions for the multidimensional integrable equations and its perturbations. Contemporary mathematics. Fundamental trend. 2004, v11, p.3-149 (PDF-file in Russian). S.G. Glebov, O.M. Kiselev, V.A. Lazarev. Resonant pumping in nonlinear Klein-Gordon equation and solitary packets of waves. ArXiv: math-ph # 0410041. O.M. Kiselev, S.G. Glebov. Scattering of solitons on resonance. Asymptotics and numeric simulations. ArXiv: nlin.PS # 0410024. O.M. Kiselev, S.G. Glebov. 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, pp.109-134. Publishing by Georgian Academy of Sciences, Institute of cybernetics, Tbilisi, 2003. 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. (PDF-file) 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. Matematicheskaya fizika, Analiz, Geometriya, 2002, v.9, n2, pp.272-280. O.M. Kiselev. Krylov-Bogolyubov ansatz for nonlinear nonautonomous second order equation. Review. 22 pages (in Russian). DVI-file (196kB), PS-file (594kB) 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, S107-S139. (PDF-file) 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. В кн. Complex Analysis, Differential Equations and related topics. Differential Equations. I. Ufa, 2000, p.49-52. (in Russian) O.M. Kiselev, S.G. Glebov. Asymptotics of a rigid generation of natural oscillations. II В кн. Complex Analysis, Differential Equations and related topics. Differential Equations. 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, n2, p.345-358. O.M. Kiselev. Asymptotic behaviour of a solution for Kadomtsev-Petviashvili-2 equation. ArXiv: math-ph # 0003014. O.M. Kiselev. Asymptotics of soliton solution for the perturbed Davey-Stewartson-I equations. ArXiv: math-ph # 9909028. R.R.Gadyl'shin, O.M. Kiselev. Structural instability of soliton for the Davey-Stewartson II equation. Teor. Mat. Fiz., 1999, v.118, n3, 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, n2, 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. ArXiv: 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. ArXiv: solv-int # 9902004. O.M. Kiselev. The basic functions associated with a two-dimensional Dirac system. Funk. analiz i ego pril., 1998, v.32, n1, p.72-76 (in Russian). R.R. Gadyl'shin, O.M. Kiselev. Asymptotics of perturbed soliton solution for the Davey-Stewartson II equation. ArXiv: solv-int # 9801014. R.R. Gadyl'shin, O.M. Kiselev. On lump instability of the Davey-Stewartson II equation. ArXiv: 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. Mat. Fiz., 1998, v.114, n1, p.104-114. O.M. Kiselev. Asymptotic behavior of the nonsoliton solution of the Davey-Stewartson II equation. Differentsialnye Uravneniya, 1997, v.33, n6, 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). (see also ArXiv: solv-int # 9701014). 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, n5, p.230. (Materials of International Conference "Differential equations and related topics" dedicated to the 95th anniversary of I.G. Petrovsky) R.R.Gadyl'shin, O.M. Kiselev. On solitonless structure of the scattering data for perturbed two-dimensional soliton solution for the Davey-Stewartson II equation. Theor. and Mathem. Phys, 1996, v.106, n2, p.200-208 (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, 1995, p. 52-70 (in Russian). O.M. Kiselev. Asymptotics of a multiple Cauchy integral with rapidly oscillating exponential. Mathematical Notes, 1995, v.58, n2, p.231-242. O.M. Kiselev. Solution of Goursat problem for the Maxwell - Bloch system. Theor. Math. Phys., 1994, v.98, n1. p.29-37. 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. Theor. Math. Phys, 1992, v.93, p.1106-1111. 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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	Theses

	O.M.Kiselev. Many-dimensional nonlinear integrable equations: asymptotic behaviour of solutions and perturbations. Doctoral thesis. Ufa 2001. Author's abstract of doctoral thesis (in Russian) Thesis (in Russian). Zipped PS-file (516 kB), Zipped DVI-file (264 kB) O.M.Kiselev. Asymptotic behaviour of solution for Cauchy problem for semi-linear perturbed hyperbolic equations. Ph.D. thesis. Ufa 1992. Author's abstract of PhD thesis (djvu 2MB) (in Russian)
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