  In this letter, we develop a Newtonian approach to the collapse of galaxy
fluctuations of scalar field dark matter under initial conditions inferred from
simple assumptions. The full relativistic system, the so called
Einstein-Klein-Gordon, is reduced to the Schr\"odinger-Newton one in the weak
field limit. The scaling symmetries of the SN equations are exploited to track
the non-linear collapse of single scalar matter fluctuations. The results can
be applied to both real and complex scalar fields.
