  We analyze the damping of the transverse breathing mode in an elongated trap
at ultralow temperatures. The damping occurs due to the parametric resonance
entailing the energy transfer to the longitudinal degrees of freedom. It is
found that the nonlinear coupling between the transverse and discrete
longitudinal modes can result in an anomalous behavior of the damping as a
function of time with the partially reversed pumping of the breathing mode. The
picture revealed explains the results observed in [16].
