  We study the theory of a (global) texture with DBI-like Lagrangian, the
higher-dimensional generalization of the previously known chiral Born-Infeld
theory. This model evades Derrick's theorem and enables the existence of
solitonic solutions in arbitrary D-dimensions. We explicitly show the solutions
in spherically-symmetric ansatz. These are examples of extended topological
solitons. We then investigate the coupling of this theory to gravity, and
obtain the static self-gravitating solitonic p-brane solutions. These
non-singular branes can be identified as the smooth versions of cosmic p-branes
which, in the thin-wall limit, suffers from naked singularities.
