  This work tries to find out thick brane solutions in braneworld scenarios
described by a real scalar field in the presence of a scalar-kinetic term
$F(X,\phi)=X\phi^m$ with a single extra dimension, where
$X=\frac12\nabla_M\phi\nabla^M\phi$ stands for the standard kinetic term and
$m=0,1,2\cdots$. We mainly consider bent branes, namely de Sitter and Anti-de
Sitter four-dimensional slices. The solutions of a flat brane are obtained when
taking the four-dimensional cosmological constant $\Lambda_4\rightarrow 0$.
When the parameter $m=0$, these solutions turn to those of the standard
scenario. The localization and spectrum of graviton on these branes are also
analyzed.
