"By applying intuition, we propose that the observed rotation curve profile in the dark matter region is of the form v
φ = αr exp(−k1r) + β[1 − exp(−k2r)]."
I'm no physicist, but I don't think papers are supposed to "apply intuition" to come up with stuff like that.
We in the "biz" call this an "assumption". You assume that for arguments sake, plug it into your models and see what predictions that gets you.