  We consider a 5-D gravity plus a bulk scalar field, and with a 3-brane. The
Darboux transformation is used to construct some exact solutions. To do this we
reduce the system of equations, which describes the 5-D gravity and bulk scalar
field to the Schr\"odinger equation. The jump conditions at the branes lead to
the jump potential in the Schr\"odinger equation. Using the Darboux
transformation with these jump conditions, we offer a new exact solution of the
brane equations, which represents a generalization of the Rundall-Sundrum
solution. For simplicity, the main attention is focused on the case when Hubble
root on the visible brane is zero. However, the argument is given that our
method is valid in more realistic models with cosmological expansion.
