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Theoretical and Mathematical Physics

, Volume 150, Issue 3, pp 347–354 | Cite as

Dipole approximation in three-vortex dynamics

  • A. S. Romanov
Article

Abstract

We solve the problem of the relative motion of two nearby vortices (a dipole pair) and a third vortex for different current functions.

Keywords

three-vortex dynamics dipole vortex integrable systems 

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References

  1. 1.
    A. V. Borisov, I. S. Mamaev, and M. A. Sokolovskii, eds., Fundamental and Applied Problems in the Theory of Vortices [in Russian], Intitute for Computer Research, Moscow (2003).Google Scholar
  2. 2.
    P. G. Saffman, Vortex Dynamics, Cambridge Univ. Press, Cambridge (1992).zbMATHGoogle Scholar
  3. 3.
    G. Blatter, M. V. Feigel’man, V. B. Geshkenbein, A. I. Larkin, and V. M. Vinokur, Rev. Modern Phys., 66, 1125 (1994).CrossRefADSGoogle Scholar
  4. 4.
    A. S. Kingsep, K. V. Chukbar, and V. V. Yan’kov, “Electronic magnetic hydrodynamics,” in: Problems in Plasma Theory (B. B. Kadomtsev, ed.), Vol. 16, Consultants Bureau, New York (1990), p. 243.Google Scholar
  5. 5.
    V. I. Arnold, Mathematical Methods of Classical Dynamics [in Russian] (3rd ed.), Éditorial URSS, Moscow (2003); English transl.: Mathematical Methods of Classical Mechanics, Springer, Berlin (1978).Google Scholar
  6. 6.
    E. A. Novikov, JETP, 41, 937 (1975).ADSGoogle Scholar
  7. 7.
    H. Aref, Phys. Fluids, 22, 393 (1979).zbMATHCrossRefADSGoogle Scholar
  8. 8.
    L. B. Okun’, Physics of Elementary Particles [in Russian], Nauka, Moscow (1988).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • A. S. Romanov
    • 1
  1. 1.Russian Research Center Kurchatov InstituteMoscowRussia

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