A Bose-Einstein condensate (BEC) is the state of matter of bosonic particles at ultra-cold temperatures. The Gross-Pitaevskii (GP) equation, a variant of the nonlinear Schro_dinger equation (NLS) that includes an external trapping, is effectively described by the mean-field dynamical properties of BECs. Experimental progress has been possible to create BECs with particles with a strong dipolar moment, as in chromium, __Cr. The dipole-dipole interaction adds a nonlocal term to the GP equation in the form of a convolution. Previous work has focused on vortex nucleation in non-dipolar condensates by dragging impurities through the condensate at supercritical speeds. For a one-dimensional GP equation with no external potential nor dipolar effects, a critical velocity can be found analytically above which dark (grey) solitons are emitted from the moving impurity. However, the case pertaining to the supercritical velocity for nucleation in dipolar condensates has yet to be considered. In this thesis, we present analytical approximations and numerical results for the critical velocity at which nucleation of dark solitons occurs in the one-dimensional dipolar GP equation.
