  The semiclassical propagator in the representation of SU(n) coherent states
is characterized by isolated classical trajectories subjected to boundary
conditions in a doubled phase space. In this paper we recast this expression in
terms of an integral over a set of initial-valued trajectories. These
trajectories are monitored by a filter that collects only the appropriate
contributions to the semiclassical approximation. This framework is suitable
for the study of bosonic dynamics in n modes with fixed total number of
particles. We exemplify the method for a Bose-Einstein condensate trapped in a
triple-well potential, providing a detailed discussion on the accuracy and
efficiency of the procedure.
