  New soliton solutions for thick branes in 4 + 1 dimensions are considered in
this article. In particular, brane models based on the sine-Gordon (SG),
$\varphi^{4}$ and $\varphi^{6}$ scalar fields are investigated; in some cases
$Z_{2}$ symmetry is broken. Besides, these soliton solutions are responsible
for supporting and stabilizing the thick branes. In these models, the origin of
the symmetry breaking resides in the fact that the modified scalar field
potential may have non-degenerate vacuua and these non-degenerate vacuua
determine the cosmological constant on both sides of the brane. At last, in
order to explore the particle motion in the neighborhood of the brane, the
geodesic equations along the fifth dimension are studied.
