NONLINEAR SCHRODINGER-EQUATION FOR SUPERCONDUCTORS

Using the Hartree-Fock-Bogoliubov factorization of the density matrix and the Born-Oppenheimer approximation we show that the motion of a su perconducting condensate satisfies a Schrodinger equation at zero temp erature. The Galilean invariance of the equation is explicitly manifes ted. This equation gives a unified description of the condensate dynam ics, such as Josephson effects, vortex dynamics and the Bogoliubov-And erson mode.