S.G. Glebov, O.M. Kiselev, N. Tarkhanov.Nonlinear equations with small parameter. Volume I: Oscillations and resonances
De Gruyter Series in Nonlinear Analysis and Applications. 2017, v. 23/1, pp.340. ISBN 978-3-11-033568-2
S.G. Glebov, O.M. Kiselev, N. Tarkhanov.Nonlinear equations with small parameter.Volume 2. Waves and boundary problems
De Gruyter Series in Nonlinear Analysis and Applications, 2018, v. 23/2, pp.424. ISBN: 978-3-11-053497-9.
O. M. Kiselev. Hard Loss of Stability in Painleve-2 Equation // Journal of Nonlinear Mathematical Physics, 2001, v. 8, no. 1, p. 65–95.
O.M. Kiselev, Asymptotics of solutions of higher-dimensional integrable equations and their perturbations
Journal of Mathematical Sciences, November 2006, Volume 138, Issue 6, pp 6067–6230 Springer
O. M. Kiselev, S. G. Glebov, “An asymptotic solution slowly crossing the separatrix near a saddle-center bifurcation point”, Nonlinearity, 16 (2003), 327-362
R. R. Gadyl'shin, O. M. Kiselev, “On nonsolution structure of scattering data under perturbation of two-dimensional soliton for Davey–Stewartson equation II”, Theoret. and Math. Phys., 106:2 (1996), 167–173
3.
R. R. Gadyl'shin, O. M. Kiselev, “Structural instability of a soliton for the Davey–Stewartson II equation”, Theoret. and Math. Phys., 118:3 (1999), 278–284
4.
S. G. Glebov, O. M. Kiselev, V. A. Lazarev, “Slow passage through resonance for a weakly nonlinear dispersive wave.”, SIAM Journal of Applied Mathematics, 65:6 (2005), 2158-2177
O. M. Kiselev, “Perturbation of a solitary wave of the nonlinear Klein–Gordon equation”, Siberian Math. J., 41:2 (2000), 281–293
8.
S. G. Glebov, O. M. Kiselev, V. A. Lazarev, “Birth of solitons during passage through local resonance”, Proc. Inst. Math. Mech., 2003no. , suppl. 1, S84–S90
9.
O. M. Kiselev, “Basic Functions Associated with a Two-Dimensional Dirac System”, Funct. Anal. Appl., 32:1 (1998), 56–59
10.
O. M. Kiselev, “An asymptotic solution of the Cauchy problem for the Davey–Stewartson-I equation”, Theoret. and Math. Phys., 114:1 (1998), 81–89
11.
S. G. Glebov, O. M. Kiselev, “The stimulated scattering of solitons on a resonance.”, Journal of Nonlinear Mathematical Physics, 12:3 (2005), 330-341
O. M. Kiselev, “Asymptotic behavior of the solution of a system of Davey–Stewartson II equations in the soliton-free case”, Differ. Equ., 33:6 (1997), 815–823
Sergei Glebov, Oleg Kiselev, and Nikolai Tarkhanov, “Weakly Nonlinear Dispersive Waves under Parametric Resonance Perturbation.”, Studies in Applied Mathematics,, 124:1 (2010), 19-37 10.1111/j.1467-9590.2009.00460.x
S. G. Glebov, O. M. Kiselev, V. A. Lazarev, “The autoresonance threshold in a system of weakly coupled oscillators”, Proc. Inst. Math. Mech., 259, suppl. 2 (2007), S111–S123
20.
O. M. Kiselev, “Asymptotic behaviour of the solution of the two-dimensional Dirac system with rapidly oscillating coefficients”, Sb. Math., 190:2 (1999), 233–254
21.
O. M. Kiselev, “Stable Feedback Control of a Fast Wheeled Robot”, Nelineinaya dinam., 14:3 (2018), 409–417
O. Kiselev, N. Tarkhanov, “The capture of a particle into resonance at potential hole with dissipative perturbation.”, Chaos, Solitons & Fractals, 58 (2014), 27-59
O. M. Kiselev, “Asymptotics of a multiple Cauchy integral with rapidly oscillating exponential”, Math. Notes, 58:2 (1995), 833–840
25.
O. M. Kiselev., “An asymptotic structure of the bifurcation boundary of the perturbed Painleve-2 equation”, Chaos, Solitons & Fractals, 151 (2021), 111299
O. M. Kiselev, V. Y. Novokshenov, “Emergence and Decay of PI-Kinks in the Sine-Gordon Model with High-Frequency Pumping”, J Math Sci, 251 (2021), 175-189
O. M. Kiselev, “Asymptotic behaviour of measure for captured trajectories into parametric autoresonance.”, Nonlinear Dynamics, 91:3 (2018), 1977-1983https://link.springer.com/article/10.1007
O. M. Kiselev, V. Yu. Novokshenov, “Emergence and Decay of $\pi$-Kinks in the Sine-Gordon Model with High-Frequency Pumping”, J. Math. Sci. (N. Y.), 252:2 (2021), 175–189
31.
O. Kiselev, N. Tarkhanov, “Scattering of trajectories at a separatrix under autoresonance.”, J. Math. Phys., 55:6 (2014), 063502
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, 362:2 (2010), 393-400http://dx.doi.org/10.1016/j.jmaa.2009.08.039
S. G. Glebov, O. M. Kiselev., “The slowly passage through the resonances and wave packets with the different carriers.”, Dynamics of Partial Differential Equations, 2:3 (2005), 261
O. M. Kiselev, “Asymptotics of a solution of the Kadomtsev-Petviashvili-2 equation”, Proceedings of the Steklov Institute of Mathematics., S:1 (2001), 107-139
36.
P. Y. Astafyeva, O. M. Kiselev, “Formal Asymptotics of Parametric Subresonance”, Rus. J. Nonlin. Dyn., 18:5 (2022), 927-937http://nd.ics.org.ru/nd221220/
37.
O. M. Kiselev, “Uniform Asymptotics of the Elliptic Sine”, J Math Sci, 258 (2021), 23-36
38.
O. M. Kiselev, Integral formulas for Painlevé-2 transcendent, 2021 (Published online) , 21 pp., arXiv: arXiv:2103.09871
39.
P. Y. Astafyeva, O. M. Kiselev, Subresonant solutions of the linear oscillator equation, 2021 , 8 pp., arXiv: arXiv:2104.00992
40.
O. M. Kiselev, “Stochastic Properties of an Inverted Pendulum on a Wheel on a Soft Surface.”, 13 pages, 13th Chaotic Modeling and Simulation International Conference. (CHAOS 2020.), Springer Proceedings in Complexity., eds. Skiadas C.H., Dimotikalis Y., Springer, 2021 (to appear) https://link.springer.com/chapter/10.1007
41.
P. Yu. Astafyeva, O. M. Kiselev, “Subresonant Solutions of the Linear Oscillator Equation”, Proc. of the Internat. Conf. on Nonlinearity, Information and Robotics (Innopolis, Russia, Aug 2021), IEEE, 2021, 90–94https://ieeexplore.ieee.org/document/9666062
42.
O. M. Kiselev, “Estimation of computational complexity for sub-optimal swarm control in non-cooperative games”, 2020 4th Scientific School on Dynamics of Complex Networks and their Application in Intellectual Robotics (DCNAIR) (Innopolis, Russia, 7-9 Sept. 2020), IEEE, 2020, 133-134
43.
O. M. Kiselev, Stochastic properties of an inverted pendulum on a wheel on a soft surface, 2020 , 16 pp., arXiv: arxiv:2006.06222
44.
O. M. Kiselev, Stabilization of the wheeled inverted pendulum on a soft surface, 2020 , 20 pp., arXiv: arxiv:2006.05450
45.
S.G.Glebov, O.M.Kiselev, N. Tarkhanov, Nonlinear equations with small parameters, v. 2, Series in Nonlinear Analysis and Applications, 23, Waves and boundary problems, De Gruyter, Berlin, New-York, 2018 , 424 pp.
46.
S.G. Glebov, O.M.Kiselev, N.Tarkhanov, Nonlinear equations with small parameter, v. 1, Series in Nonlinear Analysis and Applications, 23, Oscillations and resonances, De Gruyter, Berlin, New-York, 2017 , 337 pp.
O. M. Kiselev, Asymptotic behaviour of measure for captured trajectories into parametric autoresonance, 2016 (Published online) , 13 pp., arXiv: arXiv:1612.08426
49.
O. M. Kiselev, “Asymptotics of an autoresonance soliton”, Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 75–84
50.
Oleg Kiselev, Uniform asymptotic behaviour of Jacobi-$\sn$ near a singular point. The Lost formula from handbooks for elliptic functions, 2015 , arXiv: 1510.06602
51.
A. Vict. Antoniouk, O. M. Kiselev, N. N. Tarkhanov, “Asymptotic Solutions of the Dirichlet Problem for the Heat Equation at a Characteristic Point”, Ukrainian Mathematical Journal, 66:10 (2015), 1455-1474
52.
O. M. Kiselev, Autoresonant soliton and decay pumping, 2013 , arXiv: arXiv:1301.6885
53.
O. M. Kiselev, Threshold values of autoresonant pumping, 2013 , arXiv: 1303.4691
54.
A. Antoniouk, O. Kiselev, V. A. Stepanenko, and N. Tarkhanov, Asymptotic Solutions of the Dirichlet Problem for the Heat Equation at a Characteristic Point, Institut fur Mathematik Universitat Potsdam, October 10, 2012., Potsdam, 2012
55.
S. Glebov, O. Kiselev, N. Tarkhanov, “Forced nonlinear resonance in a system of coupled oscillators”, Chaos, 21:2 (2011), 023109 , 7 pp.
56.
Oleg Kiselev, and Nikolai Tarkhanov, Scattering of autoresonance trajectories upon a separatrix, Institut fur Mathematik Universitat Potsdam, Potsdam, 2011
57.
Sergei Glebov, Oleg Kiselev, Nikolai Tarkhanov, Autoresonance in a Dissipative System., 2009 , arXiv: 0912.0133
58.
O. M. Kiselev, Oscillations near separatrix for perturbed Duffing equation., 2009 , arXiv: 0903.4523
59.
Oleg Kiselev, Sergei Glebov, Autoresonant germ in dissipative system., 2009 , arXiv: 0902.4595
60.
S. G. Glebov, O. M. Kiselev, V. A. Lazarev, The autoresonance threshold into a system of weakly coupled oscillators., 2007 , arXiv: 0707.2311
61.
S. G. Glebov, O. M. Kiselev, “Rezonansnoe vozbuzhdenie voln v uravnenii KdF.”, Sbornik materialov nauchnogo seminara stependiatov programmy “Mikhail Lomonosov” 2005/06. DAAD - Min. Nauki i Obrazovaniya-Germanskaya sluzhba nauchnykh obmenov. Moskva, 24-25 aprelya 2006 g., s.38-41., 2006, 38-41
62.
N. K. Gorbatova, O. M. Kiselev, S. G. Glebov., Finite amplitude waves under a small resonant driving force, 2005 , arXiv: nlin.PS/0512049
63.
O. M. Kiselev, S. G Glebov, The capture into parametric autoresonance, 2005 , arXiv: math-ph # 0511017
64.
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,, Potsdam,, 2005
65.
O. M. Kiselev, “Asymptotics of solutions of higher-dimensional integrable equations and their perturbations”, Journal of Mathematical Sciences, 138:6 (2006), 6067–6230
66.
S. G. Glebov, O. M. Kiselev, V. A. Lazarev, Resonant pumping in nonlinear Klein-Gordon equation and solitary packets of waves, 2004 , arXiv: math-ph # 0410041
67.
O. M. Kiselev, S. G. Glebov., Scattering of solitons on resonance. Asymptotics and numeric simulations., 2004 , arXiv: nlin.PS # 0410024
68.
O. M. Kiselev, S. G. Glebov, Scattering of solitons on resonance., 2004 , arXiv: math-ph # 0403038
69.
O. M. Kiselev, “Mnogomernye nelineinye integriruemye uravneniya: asimptotiki reshenii i vozmuscheniya.”, Asimptoticheskie metody funktsionalnogo analiza,, Sovremennaya matematika i ee prilozheniya., 5, Akademiya nauk Gruzii, Institut kibernetiki, Tbilisi,, 2003, 109-134
70.
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”,, St.Petersburg Dept. Steklov' Math. Inst., SPb, 2003, 46-51
71.
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., Mathematical problem of nonlinear dynamics,, 1, Nizhny Novgorod, 2002, 269-274
72.
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., 9:1 (2002), 60-83
73.
O. M. Kiselev, S. G. Glebov.., Asymptotic decsription of nonlinear resonance, 2001 , arXiv: math.DS # 0105011
74.
O. M. Kiselev, Mnogomernye nelineinye integriruemye uravneniya: asimptotiki reshenii i vozmuscheniya., Diss. dokt. fiz.-matem. nauk, IMVTs UNTs RAN, Ufa, 2001
75.
S. G. Glebov, O. M. Kiselev, “Asimptotika zhestkogo rezhima vozbuzhdeniya sobstvennykh kolebanii. I.”, Kompleksnyi analiz, differentsialnye uravneniya i smezhnye voprosy. Differentsialnye uravneniya. Chast I., Ufa, 2000, 49-52
76.
O. M. Kiselev, S. G. Glebov, “Asimptotika zhestkogo rezhima vozbuzhdeniya sobstvennykh kolebanii. II”, Kompleksnyi analiz, differentsialnye uravneniya i smezhnye voprosy. Differentsialnye uravneniya. Chast I., Ufa, 2000, 95-97
77.
O. M. Kiselev, Asymptotic behaviour of a solution for Kadomtsev-Petviashvili-2 equation., 2000 , arXiv: math-ph # 0003014.
78.
O. M. Kiselev, Asymptotics of soliton solution for the perturbed Davey-Stewartson-I equations, 1999 , arXiv: math-ph # 9909028
79.
O. M. Kiselev, Asymptotic approach for the rigid condition of appearance of the oscillations in the solution of the Painleve-2 equation., 1999 , arXiv: solv-int # 9902007
80.
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, solv-int # 9902004., 1999
81.
R. R. Gadyl'shin, O. M. Kiselev, Asymptotics of perturbed soliton solution for the Davey-Stewartson II equation., 1998 , arXiv: solv-int # 9801014
82.
R. R. Gadyl'shin, O. M. Kiselev, On lump instability of the Davey-Stewartson II equation., 1998 , arXiv: solv-int # 9804001
83.
O. M. Kiselev, “The interaction of a kink with a breather of small amplitude in the phi^4-model.”, Russian Journ. of Math.Phys., 5:1 (1997), 29-46
84.
O.M. Kiselev., “Metod Fure dlya linearizovannogo uravneniya Devi-Styuartsona I.”, Kompleksnyi analiz, differentsialnye uravneniya, chislennye metody i prilozheniya. III. Differentsialnye uravneniya., IMVTs, 1996, 93-97http://arxiv.org/abs/solv-int/9701014
85.
O. M. Kiselev., “Bazisnye funktsii, svyazannye s dvumernoi sistemoi Diraka.”, (Mezhdunarodnaya konferentsiya “Differentsialnye uravneniya i smezhnye voprosy”, posvyaschennaya 95-letiyu so dnya rozhdeniya I. G. Petrovskogo: sovmestnye zasedaniya seminara imeni I. G. Petrovskogo i Moskovskogo matematicheskogo obschestva; vosemnadtsataya sessiya, 25–29 aprelya 1996 goda), Uspekhi matem. nauk, 51, no. 5, 1996, 230
86.
O. M. Kiselev, “Asimptotika resheniya zadachi Koshi dlya polulineinoi giperbolicheskoi sistemy s silnoi dispersiei.”, Asimptotiki i simmetrii v nelineinykh dinamicheskikh sistemakh, IMVTs, Ufa, 1995, 52-70
87.
O. M. Kiselev, “Formalnoe reshenie zadachi Gursa dlya uravneniya sinus-Gordon.”, Integriruemost v dinamicheskikh sistemakh., IMVTs, Ufa, 1994, 17-26
88.
O. M. Kiselev, “Ob asimptotike kratnogo integrala tipa Fure”, Asimptoticheskie metody reshenii differentsialnykh uravnenii, IMVTs, Ufa, 1992, 61-73
89.
O. M. Kiselev, Asimptotika resheniya zadachi Koshi dlya polulineinykh giperbolicheskikh uravnenii, Diss. kand. fiz.-matem. nauk, IMVTs UNTs RAN, Ufa, 1992
90.
O. M. Kiselev“.Formalnaya asimptotika solitonnogo resheniya vozmuschennogo uravneniya Sine-Gordon.”, Asimptoticheskie resheniya zadach matematicheskoi fiziki, IMVTs, Ufa, 1990, 50-62
91.
O. M. Kiselev, “Asimptotika resheniya zadachi Koshi dlya redutsirovannoi sistemy Maksvella-Blokha.”, Asimptoticheskie metody reshenii zadach matematicheskoi fiziki, BashFAN, Ufa, 1989, 70-81
92.
O. M. Kiselev, “Asimptotika resheniya zadachi Koshi dlya vozmuschennogo uravneniya Kleina-Foka-Gordona.”, Zapiski Nauchn. Semin. LOMI, 165 (1987) , 115-121 pp.
93.
O. M. Kiselev, “Boundaries of computational complexity and optimal cluster's quantity for controlled swarm in non-cooperative games”, Izvestiya vuzov. PND, 29:3 (2021), 376–385;
94.
O. M. Kiselev, “Ravnomernaya asimptotika funktsii sinus amplitudy”, Differentsialnye uravneniya, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 163, VINITI RAN, M., 2019, 25–38
95.
O. M. Kiselev, V. Yu. Novokshenov, “Autoresonance in a model of a terahertz wave generator”, Proc. Steklov Inst. Math. (Suppl.), 301, suppl. 1 (2018), 88–102
96.
Z. N. Validova, O. M. Kiselev, “Integrals obtained from a singular Hilbert integral by a change of variables”, Russian Math. (Iz. VUZ), 36:9 (1992), 13–21
97.
I. G. Gazheev, O. M. Kiselëv, “On the problem of continuous flow around a closed cylindrical shell”, Soviet Math. (Iz. VUZ), 28:10 (1984), 32–41
98.
O. M. Kiselev, Matematicheskie osnovy robototekhniki, Universitet Innopolis, Orel: Izdatelstvo «Kartush», 2019. – 228 s., 2019 , 228 pp.
99.
O. M. Kiselev, Zoopark chudovisch ili znakomstvo so spetsialnymi funktsiyami, BashGU, Ufa, 2012 , 104 pp.
100.
O. M. Kiselev, Lektsii po teorii nelineinykh kolebanii, Bashgosuniversitet, Ufa, 2006 , 136 pp.
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