  In the model of a gravitating system with two scalar fields (one of which is
phantom), two new types of regular solutions are found: mechanism for
compactification of an extra dimension and a flat thick brane solution. It is
shown that the first model has solutions oscillating over the extra coordinate
and giving a finite radius of compactification of the fifth dimension and the
second model is a flat thick brane embedded in the 5D Minkowski spacetime.
Geometry of both models corresponds to a five-dimensional Minkowski space-time.
Consideration of linear perturbations shows stability of the obtained
solutions.
