Wave guide perturbative solutions for the Ginzburg-Landau equation. Infinite conductivity and discrete values of the critical temperature in superconductors

We build perturbative solutions of the Ginzburg-Landau equation in the strong coupling limit, in terms of the elliptic functions cn and dn, Breaking of the soliton in 'soliton trains' is envisaged as a phenomenon similar to 'self-channeling' from the non-linear waves theory. Generalizing this last result for a cylindrical geometry, waves associated with the superconducting charge carriers are assimilated to a homogeneous wave family, namely a self-maintained wave guide. We state that wave guide perturbative solutions of the Ginzburg-Landau equation in the strong coupling limit account for the infinite conductivity and prompt for discrete values of the critical temperature in superconductors. (C) 1999 Elsevier Science B.V. All rights reserved.