[en] Recently we proposed that K fields, that is, fields with a non-standard kinetic term, may provide a mechanism for the generation of thick branes, based on the following observations. First, K field theories 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. Second, propagation of linear perturbations is confined inside the compacton domain wall. Further, these linear perturbations inside the topological defect are of the standard type, in spite of the non-standard kinetic term. Third, when gravity is taken into account, location of gravity in the sense of Randall-Sundrum works for these compacton domain walls provided that the backreaction of gravity does not destabilize the compacton domain wall. It is the purpose of the present paper to investigate in detail the existence and stability of compacton domain walls in the full K field and gravity system, using both analytical and numerical methods. We find that the existence of the domain wall in the full system requires a correlation between the gravitational constant and the bulk cosmological constant