  When two Bose-Einstein condensates (BEC's) collide with high collisional
energy, the celebrated matter wave interference pattern results. For lower
collisional energies the repulsive interaction energy becomes significant, and
the interference pattern evolves into an array of grey solitons. The lowest
collisional energy, producing a single pair of solitons, has not been probed.
We use density engineering on the healing length scale to produce such a pair
of solitons. These solitons then evolve periodically between vortex rings and
solitons, which we image in-situ on the healing length scale. The stable,
periodic evolution is in sharp contrast to the behavior of previous
experiments, in which the solitons decay irreversibly into vortex rings via the
snake instability. The evolution can be understood in terms of conservation of
mass and energy in a narrow condensate. The periodic oscillation between two
qualitatively different forms seems to be a rare phenomenon in nature.
