  We review the appearance of multiple scalar fields in linearized SFT based
cosmological models with a single non-local scalar field. Some of these local
fields are canonical real scalar fields and some are complex fields with
unusual coupling. These systems only admit numerical or approximate analysis.
We introduce a modified potential for multiple scalar fields that makes the
system exactly solvable in the cosmological context of Friedmann equations and
at the same time preserves the asymptotic behavior expected from SFT. The main
part of the paper consists of the analysis of inhomogeneous cosmological
perturbations in this system. We show numerically that perturbations
corresponding to the new type of complex fields always vanish. As an example of
application of this model we consider an explicit construction of the phantom
divide crossing and prove the perturbative stability of this process at the
linear order. The issue of ghosts and ways to resolve it are briefly discussed.
