  It is shown that simultaneously changing the scattering length of an
elongated, harmonically trapped Bose-Einstein condensate from positive to
negative and inverting the axial portion of the trap, so that it becomes
expulsive, results in a train of self-coherent solitonic pulses. Each pulse is
itself a non-dispersive attractive Bose-Einstein condensate that rapidly
self-cools. The axial trap functions as a waveguide. The solitons can be made
robustly stable with the right choice of trap geometry, number of atoms, and
interaction strength. Theoretical and numerical evidence suggests that such a
pulsed atomic soliton laser can be made in present experiments.
