Dynamics of excitations in Josephson media

By the "Josephson medium", we understand a two-dimensional (2D) medium, in which currents are governed by a Josephson-type rule. Vortices are the gene ric excitations in such a medium. The formal description of the medium pose s some problems since Lagrangian and Hamiltonian approaches reveal some dis crepancies, which can be avoided if more general equations are considered. The discrepancies are natural consequences of the Poisson structure associa ted with Josephson medium and the choice of canonical variables. From the p ractical point of view, the problem can be eliminated either by reducing th e number of variables or by considering a more general manifold. Taking int o account a cloud of non-interacting charged particles it leads to Josephso n-Vlasov equations. (C) 2000 Published by Elsevier Science B.V. All rights reserved.