Using the Non-linear Schrödinger Equation, we have found a new mechanism for the generation of vortices in a superfluid. This mechanism could be relevant for explaining the experimental creation of vortices by vibrations. This follows from the break-up of dark solitons in more than 1 D, which are linearly unstable, as shown by Kusnetsov and Turitsyn, Ž. Eksp. Teor. Fiz., 94 (1988) 119 (Sov Phys. JETP, 67 (1988) 1583).