  Solitons are among the most distinguishing fundamental excitations in a wide
range of non-linear systems such as water in narrow channels, high speed
optical communication, molecular biology and astrophysics. Stabilized by a
balance between spreading and focusing, solitons are wavepackets, which share
some exceptional generic features like form-stability and particle-like
properties. Ultra-cold quantum gases represent very pure and well-controlled
non-linear systems, therefore offering unique possibilities to study soliton
dynamics. Here we report on the first observation of long-lived dark and
dark-bright solitons with lifetimes of up to several seconds as well as their
dynamics in highly stable optically trapped $^{87}$Rb Bose-Einstein
condensates. In particular, our detailed studies of dark and dark-bright
soliton oscillations reveal the particle-like nature of these collective
excitations for the first time. In addition, we discuss the collision between
these two types of solitary excitations in Bose-Einstein condensates.
