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.
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