  We propose a method to split the ground state of an attractively interacting
atomic Bose-Einstein condensate into two bright solitary waves with controlled
relative phase and velocity. We analyze the stability of these waves against
their subsequent re-collisions at the center of a cylindrically symmetric,
prolate harmonic trap as a function of relative phase, velocity, and trap
anisotropy. We show that the collisional stability is strongly dependent on
relative phase at low velocity, and we identify previously unobserved
oscillations in the collisional stability as a function of the trap anisotropy.
An experimental implementation of our method would determine the validity of
the mean field description of bright solitary waves, and could prove an
important step towards atom interferometry experiments involving bright
solitary waves.
