  Motivated by recent experiments, we model the dynamics of bright solitons
formed by cold gases in quasi-1D traps. A dynamical variational ansatz captures
the far-from equilibrium excitations of these solitons. Due to a separation of
scales, the radial and axial modes decouple, allowing for closed-form
approximations for the dynamics. We explore how soliton dynamics influence atom
loss, and find that the time-averaged loss is largely insensitive to the degree
of excitation. The variational approach enables us to perform high precision
calculations of the critical atom number (ie. the maximum number of atoms that
can exist in a single soliton before the attractive forces overwhelm quantum
pressure, leading to collapse).
