ZhETF, Vol. 143,
No. 1,
p. 198 (January 2013)
(English translation  JETP,
Vol. 116, No. 1,
p. 173,
January 2013
available online at www.springer.com
)
DYNAMICS OF AN NVORTEX STATE AT SMALL DISTANCES
Ovchinnikov Yu.N.
Received: July 18, 2012
DOI: 10.7868/S0044451013010198
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 timedependent GinsburgLandau 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 , 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 Nvortex state is fixed by the position of vortices at any time instant and by the values of two small parameters. For , a new parameter arises in the problem, connected with relative increases in the number of decay modes.

