  An integrable nonlinear model for the time-dependent equilibration of a
bosonic system that has been devised earlier is solved exactly with boundary
conditions that are appropriate for a truncated Bose-Einstein distribution, and
include the singularity at $\epsilon = \mu$. The buildup of a thermal tail
during evaporative cooling, as well as the transition to the condensed state
are accounted for. To enforce particle-number conservation during the cooling
process with an energy-dependent density of states for a three-dimensional
thermal cloud, a time-dependent chemical potential is introduced.
