Solving a nonlinear analytical model for bosonic equilibration

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.