Petrov, Alexander Georgievich

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Total publications: 30
Scientific articles: 30
Presentations: 5

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Doctor of physico-mathematical sciences (1989)
Speciality: 01.02.05 (Mechanics of fluids, gases and plasmas)
Birth date: 08.07.1944
E-mail: ,
Keywords: fluid mechanics; gamiltonian mechanics; chaotic dynamics; mixing; nonlinear waves; Boussinesq–type equations.


The total integral of the Boussinesq–type equations for surface gravity long waves in the form Kulikovsky–Drozdova form is found. The equations of Kulikovsky–Drozdova published in 1996 describes waves in channel. Nonstationary flow of a viscoplastic medium between two parallel plates was considered for the case of varying pressure gradient. The problem is reduced to the Stephan problem. Four multiparameter family of exact solutions are found. The new modification of a method of an average of a Hamilton systems is offered. The method is based on analytical expression of the Poincare maps in parametrical form. The developed method gives an asymptotic solution of a problem about a spherical pendulum with arbitrary vibration of a suspension point. The motion of particles of an incompressible viscous and visco-plastic mediums in thin layer whose boundary varies in a periodic way was investigated. Transition to the globally dynamical chaos is described.


Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1966 (department of highdrodymics). Ph.D. thesis was defended in 1971. D.Sci. thesis was defended in 1989. A list of my works contains more than 100 titles and 3 monographs.

Main publications:
  • Klimov D. M., Petrov A. G. Analytical solutions of the boundary-value problem of nonstationary flow of viscoplasic medium between two plates // Archive of Applied Mechanics. V. 70. 2000. p. 3–16.
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. A. O. Zakhar'in, A. V. Andrianov, A. G. Petrov, “Stimulated terahertz emission in a system of excitons in photoexcited silicon”, Pis'ma v Zh. Èksper. Teoret. Fiz., 109:12 (2019),  821–825  mathnet  elib; JETP Letters, 109:12 (2019), 781–785  isi  scopus
2. A. G. Petrov, “Saturation-Free Numerical Scheme for Computing the Flow Past a Lattice of Airfoils with a Sharp Edge”, Nelin. Dinam., 15:2 (2019),  135–143  mathnet
3. A. O. Kazakova, A. G. Petrov, “Расчет течения вязкой жидкости между двумя произвольно движущимися цилиндрами произвольного сечения”, Zh. Vychisl. Mat. Mat. Fiz., 59:6 (2019),  1063–1082  mathnet  elib
4. A. V. Andrianov, A. O. Zakhar'in, A. G. Petrov, “Intraexciton and intracenter terahertz radiation from doped silicon under interband photoexcitation”, Pis'ma v Zh. Èksper. Teoret. Fiz., 107:9 (2018),  564–568  mathnet  elib; JETP Letters, 107:9 (2018), 540–543  isi  elib  scopus
5. Alexander Petrov, Mariana Lopushanski, Vladimir Vanovskiy, “Stability of capillary waves of finite amplitude”, Lect. Notes Electr. Eng., 428 (2018),  51–57  mathnet  scopus
6. Alexander Petrov, Mariana Lopushanski, “Ellipsoid movement in ideal or viscous fluid”, MATEC Web Conf., 211 (2018),  15004–7  mathnet  isi  scopus
7. Alexander Petrov, Mariana Lopushanski, “Study of finite amplitude capillary waves stability”, MATEC Web Conf., 211 (2018),  4008–7  mathnet  isi  scopus
8. A. G. Petrov, V. V. Vanovskiy, “Nonlinear oscillations of a spring pendulum at the 1 : 1 : 2 resonance: theory, experiment, and physical analogies”, Tr. Mat. Inst. Steklova, 300 (2018),  168–175  mathnet  elib; Proc. Steklov Inst. Math., 300 (2018), 159–167  isi  scopus
9. N. D. Baikov, A. G. Petrov, “Deformation of cylindrical cavities in plane-parallel potential flows with circulation and under the action of mass forces”, Vychisl. Metody Programm., 19:3 (2018),  207–214  mathnet
10. N. D. Baikov, A. G. Petrov, “Formation of a cumulative jet in the plane-parallel flow of a perfect fluid”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2017, 5,  42–47  mathnet; Moscow University Mechanics Bulletin, 72:5 (2017), 119–123  isi  scopus
11. A. G. Petrov, Sh. V. Sanduleanu, “Simulation of electrochemical machining using the boundary element method with no saturation”, Zh. Vychisl. Mat. Mat. Fiz., 56:10 (2016),  1810–1820  mathnet  elib; Comput. Math. Math. Phys., 56:10 (2016), 1793–1802  isi  scopus
12. A. G. Petrov, I. I. Potapov, “Computation of forces acting on bodies in plane and axisymmetric cavitation flow problems”, Zh. Vychisl. Mat. Mat. Fiz., 56:2 (2016),  318–331  mathnet  elib; Comput. Math. Math. Phys., 56:2 (2016), 320–333  isi  scopus
13. K. A. Ivanov, A. G. Petrov, M. A. Kaliteevski, A. J. Gallant, “Anharmonic Bloch oscillation of electrons in biased superlattices”, Pis'ma v Zh. Èksper. Teoret. Fiz., 102:12 (2015),  911–918  mathnet  elib; JETP Letters, 102:12 (2015), 796–802  isi  scopus
14. V. I. Sankin, A. V. Andrianov, A. O. Zahar'in, A. G. Petrov, “Terahertz radiation induced by the Wannier-Stark localization of electrons in a natural silicon carbide superlattice”, Pis'ma v Zh. Èksper. Teoret. Fiz., 94:5 (2011),  393–396  mathnet; JETP Letters, 94:5 (2011), 362–365  isi  scopus
15. A. G. Petrov, “Saturation-free numerical scheme for computing the flow past a lattice of airfoils and the determination of separation points in a viscous fluid”, Zh. Vychisl. Mat. Mat. Fiz., 51:7 (2011),  1326–1338  mathnet  mathscinet; Comput. Math. Math. Phys., 51:7 (2011), 1239–1250  isi  scopus
16. V. P. Varin, A. G. Petrov, “A hydrodynamic model of human cochlea”, Zh. Vychisl. Mat. Mat. Fiz., 49:9 (2009),  1708–1723  mathnet  zmath; Comput. Math. Math. Phys., 49:9 (2009), 1632–1647  isi  scopus
17. V. P. Varin, A. G. Petrov, “A mathematical model of human cochlea”, Keldysh Institute preprints, 2008, 096, 26 pp.  mathnet
18. A. G. Petrov, “Quadrature formulas for periodic functions and their application to the boundary element method”, Zh. Vychisl. Mat. Mat. Fiz., 48:8 (2008),  1344–1361  mathnet  mathscinet  zmath  elib; Comput. Math. Math. Phys., 48:8 (2008), 1266–1283  isi  elib  scopus
19. A. G. Petrov, S. V. Rotkin, “Energy relaxation of hot carriers in single-wall carbon nanotubes by surface optical phonons of the substrate”, Pis'ma v Zh. Èksper. Teoret. Fiz., 84:3 (2006),  185–189  mathnet; JETP Letters, 84:3 (2006), 156–160  isi  scopus
20. A. G. Petrov, “Asymptotic Methods for Solving the Hamilton Equations with the Use of a Parametrization of Canonical Transformations”, Differ. Uravn., 40:5 (2004),  626–638  mathnet  mathscinet; Differ. Equ., 40:5 (2004), 672–685
21. D. V. Georgievskii, D. M. Klimov, A. G. Petrov, “Inertialess deformation of weakly inhomogeneous viscous media”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2002, 2,  37–41  mathnet
22. A. G. Petrov, L. V. Fishkis, “Wind turbulent flow in a basin of constant depth bounded by a vertical rectangular wall”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1998, 4,  55–58  mathnet  zmath
23. A. G. Petrov, V. G. Smolyanin, “On the equation for the curvature of a curve changing in time and having a given distribution of distinguished points on it”, Uspekhi Mat. Nauk, 50:5(305) (1995),  249–250  mathnet  mathscinet  zmath; Russian Math. Surveys, 50:5 (1995), 1092–1094  isi
24. A. G. Petrov, V. G. Smolyanin, “An equation for the curvature and interpolation of a line that changes over time”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1995, 6,  69–71  mathnet  mathscinet  zmath
25. O. S. Alferov, A. G. Petrov, “Turbulent flow over rotating rough surface”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1995, 3,  60–65  mathnet  zmath
26. A. G. Petrov, V. G. Smolyanin, “Calculation of a capillary-gravity wave profile on a surface of a heavy liquid of a finite depth”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1991, 3,  92–96  mathnet  zmath
27. A. G. Petrov, “Internal circulation and deformation of viscous drops”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1988, 3,  85–88  mathnet  zmath
28. A. G. Petrov, “The resistance force acting on an axisymmetric nonthin body for small cavitation numbers”, Dokl. Akad. Nauk SSSR, 282:6 (1985),  1320–1323  mathnet  mathscinet  zmath
29. A. G. Petrov, “A direct variational method of calculating plane and axisymmetric cavitation flows”, Dokl. Akad. Nauk SSSR, 257:6 (1981),  1323–1327  mathnet  zmath
30. A. G. Petrov, “Reactions acting on a small solid in plane-parallel vortex flow”, Dokl. Akad. Nauk SSSR, 238:1 (1978),  33–35  mathnet  zmath
31. O. V. Voinov, A. G. Petrov, “The stability of a small body in a nonuniform flow”, Dokl. Akad. Nauk SSSR, 237:6 (1977),  1303–1306  mathnet  mathscinet  zmath
32. V. V. Voinov, O. V. Voinov, A. G. Petrov, “A method of calculating the potential flow of an incompressible fluid around a solid revolution”, Zh. Vychisl. Mat. Mat. Fiz., 14:3 (1974),  797–802  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 14:3 (1974), 263–268
33. O. V. Voinov, A. G. Petrov, “Lagrangian of a gas bubble in a nonuniform flow”, Dokl. Akad. Nauk SSSR, 210:5 (1973),  1036–1039  mathnet  zmath

Presentations in Math-Net.Ru
1. Параметрическое представление симмплектических матриц
A. G. Petrov
Research Seminar of the Department of Higher Algebra MSU
February 17, 2020
2. Нелинейные колебания маятника на пружине при резонансе 1:1:2. Течения, эксперимент и физические аналогии
A. G. Petrov
All-Russian conference "Modern Problems of Continuum Mechanics" devoted to 110 anniversary of L. I. Sedov
November 15, 2017 17:40
3. Численный расчет течения вязкой жидкости между двумя движущимися цилиндрами
A. G. Petrov, A. O. Kazakova
All-Russian conference "Modern Problems of Continuum Mechanics" devoted to 110 anniversary of L. I. Sedov
November 14, 2017 16:00
4. О вычислении гамильтоновой нормальной формы
A. G. Petrov
Seminar of the Department of Differential Equations, Steklov Mathematical Institute of RAS
April 23, 2008 12:00
5. Квазистационаpное движение слабонеодноpодной вязкой жидкости в тонком слое
A. G. Petrov, D. V. Georgievskii
Scientic seminar «Actual problems of geometry and mechanics » named after Prof. V.V. Trofimov
October 27, 2000 18:30

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