In this work, the current-induced inertial effects on skyrmions hosted in ferromagnetic systems are studied. {When the dynamics is considered beyond the particle-like description, magnetic skyrmions can deform due to a self-induced field. We perform Monte Carlo simulations to characterize the deformation of the skyrmion during its movement}. In the low-velocity regime, the deformation in the skyrmion shape is quantified by an effective inertial mass, which is related to the dissipative force. When skyrmions move faster, the large self-induced deformation triggers topological transitions. The transition is characterized by the proliferation of skyrmions and different total topological charge, which are obtained in terms of the skyrmion velocity. Our findings provide an alternative way to describe the skyrmion dynamics that take into account the deformations of its structure. Furthermore, the motion-induced topological phase transition brings the possibility to control the number of ferromagnetic skyrmions by velocity effects.
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