  We demonstrate that a tight transverse trap with the local frequency, $%
\omega_{\perp}$, gradually varying in the longitudinal direction ($x$) induces
an effective potential for one-dimensional solitons in a self-attractive
Bose-Einstein condensate. An analytical approximation for this potential is
derived by means of a variational method. In the lowest approximation, the
potential is $N(S+1)\omega_{\perp}(x)$, with $N$ the soliton's norm (number of
atoms), and $S$ its intrinsic vorticity (if any). The results can be used to
devise nonuniform traps helping to control the longitudinal dynamics of the
solitons. Numerical verification of the analytical predictions will be
presented elsewhere.
