Usual and phantom scalar fields in five dimensions: compactification and flat thick brane solutions

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.