  We observe the formation of shock waves in a Bose-Einstein condensate
containing a large number of sodium atoms. The shock wave is initiated with a
repulsive, blue-detuned light barrier, intersecting the BEC, after which two
shock fronts appear. We observe breaking of these waves when the size of these
waves approaches the healing length of the condensate. At this time, the wave
front splits into two parts and clear fringes appear. The experiment is modeled
using an effective 1D Gross-Pitaevskii-like equation and gives excellent
quantitative agreement with the experiment, even though matter waves with
wavelengths two orders of magnitude smaller than the healing length are
present. In these experiments, no significant heating or particle loss is
observed.
