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Leonid Kurakin 


Institute of Mathematics, Mechanics, and Computer Science named after of I.I. Vorovich


Dissertation Council 212.208.29

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Degree: Doctor of Sciences

Personal page in Russian:
Personal page in English:

Research interests:

Stability and bifurcation of the families of equilibria and stationary movements of dynamic systems with symmetry and cosymmetry

Research projects:

  1. CRDF Award Number: RUM1–2943–RO–09, N-vortex problem in applications to atmospheric events, ноябрь2009– январь2012.
  2. Analytical departmental target program "Development Scientific Potential of Higher Education(2009-2011)». Direction 1, N 01201157122 «Hydrodynamic models and studying of fluid flows», 2011.
  3.  RFBR N 11-05-01138-а«Stability and bifurcation of vortex configurations in hydrodynamic models with symmetry» , 2011–2013.
  4. Development Programm of the Federal State Autonomous Educational Institution of Higher Professional Education «Southern Federal University" Development of analytical, asymptotic and numerical methods of mathematical hydrodynamics.N213.01-24/2013-69, 2013.
  5. The state task of the Ministry of Education and Science of the Russian Federation ("Fundamental problems of vortex and wave dynamics"N 1.5139.2011), 2012–2013.

Key publications:

  1. Kurakin L.G., Ostrovskaya I.V., Sokolovskiy M.A. On the stability of discrete tripole, quadrupole, Thomson’vortex triangle and square in a two-layer/homogeneous rotating fluid // Regul. Chaotic Dyn., 2016, 21 (3), 291-334.
  2. Kurakin, L., Melekhov, A., Ostrovskaya, I. A survey of the stability criteria of Thomson’s vortex polygons outside a circular domain// Bol. Soc. Mat. Mex. (2016) 22: 733. doi:10.1007/s40590-016-0121-y
  3. Kurakin L.G., Ostrovskaya I.V., Sokolovskiy M.A. Stability of discrete vortex multipoles in homogeneous and two-layer rotating fluid // Doklady Physics, 2015, 60 (5), 217–223.
  4. Kurakin, L.G. Influence of annular boundaries on Thomson’s vortex polygon stability // Chaos. 2014. Vol.14. 023105.DOI: 10.1063/1.4870735.
  5. Kurakin, L.G. The stability of the steady rotation of a system of three equidistant vortices outside a circle // J. of Appl. Math. and Mech. 2011. Т. 75. N 2. С. 227-234.
  6. Kurakin L.G., Ostrovskaya I.V. Stability of the Thomson vortex polygon with evenly many vortices outside a circular domain // Siberian Mathematical Journal. 2010. Т. 51. N 3. С. 463-474.
  7. Kurakin, L.G., Ostrovskaya, I.V. Nonlinear Stability Analysis of a Regular Vortex Pentagon Outside a Circle // Regular and Chaotic Dynamics. 2012. Vol. 17, No. 5. P. 385-396.
  8. Kurakin, L.G. On the Stability of Thomson’s Vortex Configurations Inside a Circular Domain // Regular and Chaotic Dynamics. 2010. Vol. 15, No. 1. P. 40-58.
  9. Kurakin L.G. On stability of a regular vortex polygon in the circular domain // J. Math. Fluid Mech. 2005. V. 7. Suppl. 3, p. S376-S386.
  10. Kurakin L.G. On nonlinear stability of the regular vortex systems on a sphere // Chaos. 2004. V. 14. N 3. P. 592-602.
  11. Kurakin L.G. Stability, resonances, and instability of regular vortex polygons in a circular domain // Doklady Physics. 2004. Т. 49. N 11. С. 658-661.
  12. Kurakin L.G., Yudovich V.I. The stability of stationary rotation of a regular vortex polygon // Chaos. 2002. V. 12. Iss. 3. P. 574-595.