  In this paper, we will describe the idea that dark matter partly consists of
gravitational solitons (gravisolitons). The corresponding solution is valid for
weak gravitational fields (weak field limit) with respect to a background
metric. The stability of this soliton is connected with the existence of a
special foliation and amazingly with the smoothness properties of spacetime.
Gravisolitons have many properties of dark matter, such as no interaction with
light but act on matter via gravitation. In this paper, we showed that the
gravitational lensing effect of gravisolitons agreed with the lensing effect of
usual matter. Furthermore, we obtained the same equation of state $w=0$ as
matter.
