DYNAMICS OF AN N-VORTEX STATE AT SMALL DISTANCES
Ovchinnikov Yu.N.

Received: July 18, 2012

DOI: 10.7868/S0044451013010198

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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 , the position of the ``weight center'' weakly depends on time and is located in the range of the order of a<sup>3</sup>, 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 , a new parameter arises in the problem, connected with relative increases in the number of decay modes.