  K fields, that is, fields with a non-standard kinetic term, allow for soliton
solutions with compact support, i.e., compactons. Compactons in 1+1 dimensions
may give rise to topological defects of the domain wall type and with finite
thickness in higher dimensions. Here we demonstrate that, for an appropriately
chosen kinetic term, propagation of linear perturbations is completely
suppressed outside the topological defect, confining the propagation of
particles inside the domain wall. On the other hand, inside the topological
defect the propagation of linear perturbations is of the standard type, in
spite of the non-standard kinetic term. Consequently, this compacton domain
wall may act like a brane of finite thickness which is embedded in a higher
dimensional space, but to which matter fields are constrained. In addition, we
find strong indications that, when gravity is taken into account, location of
gravity in the sense of Randall--Sundrum works for these compacton domain
walls. When seen from the bulk, these finite thickness branes, in fact, cannot
be distinguished from infinitely thin branes.
