Relaxation of Bose-condensate oscillations in a mesoscopic system at <Emphasis Type="Italic">T</Emphasis>=0

A general system of nonlinear equations describing the nondissipative evolution of an oscillating Bose condensate is presented. The relaxation of the transverse oscillations of the condensate in a trap of cylindrical symmetry is considered. The evolution is due to the parametric resonance coupling the transverse mode with the longitudinal ones. Nonlinear rescattering in the subsystem of discrete longitudinal modes leads to the suppression of back energy recovery, generating the nondissipative nonmonotonic relaxation of the transverse oscillations of the condensate.