Journal of Experimental and Theoretical Physics

, Volume 116, Issue 1, pp 173–179 | Cite as

Dynamics of an N-vortex state at small distances

  • Yu. N. Ovchinnikov
Statistical, Nonlinear, and Soft Matter Physics


We investigate the dynamics of a state of N vortices, placed at the initial instant at small distances from some point, close to the “weight center” of vortices. The general solution of the time-dependent Ginsburg-Landau equation for N vortices in a large time interval is found. For N = 2, the position of the “weight center” of two vortices is time independent. For N ≥ 3, the position of the “weight center” weakly depends on time and is located in the range of the order of a 3, where a is a characteristic distance of a single vortex from the “weight center.” For N = 3, the time evolution of the N-vortex state is fixed by the position of vortices at any time instant and by the values of two small parameters. For N ≥ 4, a new parameter arises in the problem, connected with relative increases in the number of decay modes.


Vortex Theoretical Physic Small Distance Decay Mode Unstable Mode 
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  1. 1.
    Yu. N. Ovchinnikov and I. M. Sigal, Nonlinearity 11, 1277 (1998).MathSciNetADSzbMATHCrossRefGoogle Scholar
  2. 2.
    Yu. N. Ovchinnikov and I. M. Sigal, JETP 112(3), 469 (2011).ADSCrossRefGoogle Scholar
  3. 3.
    B. L. G. Jonsson, Yu. N. Ovchinnikov, I. M. Sigal, and F. S. T. Ting, J. Math. Phys. 52, 093505 (2011).MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Max-Planck Institute for Physics of Complex SystemsDresdenGermany
  2. 2.Landau Institute for Theoretical PhisicsRussian Academy of SciencesChernogolovka, Moscow RegionRussia

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