  In weakly nonlinear dispersive systems, solitons are spatially localized
solutions which propagate without changing shape through a delicate balance
between dispersion and self-focusing nonlinear effects. These states have been
extensively studied in Bose-Einstein condensates, where interatomic
interactions give rise to such nonlinearities. Previous experimental work with
matter wave solitons has been limited to static intensity profiles. The
creation of matter wave breathers--dispersionless soliton-like states with
collective oscillation frequencies driven by attractive mean-field
interactions--have been of theoretical interest due to the exotic behaviour of
interacting matter wave systems. Here, using an attractively interacting
Bose-Einstein condensate, we present the first observation of matter wave
breathers. A comparison between experimental data and a cubic-quintic
Gross-Pitaevskii equation suggests that previously unobserved three-body
interactions may play an important role in this system. The observation of long
lived stable breathers in an attractively interacting matter wave system
indicates that there is a wide range of previously unobserved, but
theoretically predicted, effects that are now experimentally accessible.
