  In this work we deal with a non-canonical scalar field in the two-dimensional
spacetime. We search for a generalized model that is twin of the standard
model, supporting the same defect structure with the same energy density. We
also study the stability of the defect solution under small fluctuations, which
is governed by a Sturm-Liouville equation, and show how to make it stable. The
model is then modified and used in the five-dimensional spacetime to construct
a thick brane that engenders the first order framework and preserves the
twinlike behavior, under tensorial fluctuations of the metric in its
gravitational sector.
