I conducted my doctoral thesis under the supervision of Professor Víctor Manuel Romero Rochín at the Institute of Physics, National Autonomous University of Mexico (UNAM). The essence of my research revolved around the different outcomes derived from the dynamics and stability of topological defects in superfluid systems. We considered various scenarios and developed and applied computational methods to numerically solve the non-linear Gross-Pitaevskii equation (GPE). We correlated our results with experimental results in the field of quantum turbulence of Bose-Einstein condensates.