Abstract
In this manuscript we track the evolution of a system consisting of two self-gravitating virialized objects made of a scalar field in the Newtonian limit. The Schr\"odinger-Poisson system contains a potential with self-interaction of the Gross-Pitaevskii type for Bose condensates. Our results indicate that solitonic behavior is allowed in the scalar field dark matter model when the total energy of the system is positive, that is, the two blobs pass through each other as should happen for solitons; on the other hand, there is a true collision of the two blobs when the total energy is negative.
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