In the present work the dynamical evolution of long-lived dark solitons has been studied as a paradigm of non-linear physics for the first time. We have been able to observe oscillations of dark solitons in elongated Bose-Einstein condensates and good agreement with the theoretically predicted oscillation frequency of omega#2 has been obtained. Moreover the results of detailed studies of the collision of two dark solitons distinguished by different depths are presented. This particular feature enables the identification of the individual solitons beyond the actual collision process and as a central result we show shown that these peculiar entities interpenetrate without significantly influencing each other. The theoretical description of solitons as weakly interacting quasi particles is in good agreement with these findings. Continuative studies on vectorial "dark-bright" solitons and their dynamical properties complement the investigations on dark solitons.