  We report the bright solitons of the generalized Gross-Pitaevskii (GP)
equation with some types of physically relevant parity-time-(PT-) and
non-PT-symmetric potentials. We find that the constant momentum coefficient can
modulate the linear stability and complicated transverse power-flows (not
always from the gain toward loss) of nonlinear modes. However, the varying
momentum coefficient Gamma(x) can modulate both unbroken linear PT-symmetric
phases and stability of nonlinear modes. Particularly, the nonlinearity can
excite the unstable linear mode (i.e., broken linear PT-symmetric phase) to
stable nonlinear modes. Moreover, we also find stable bright solitons in the
presence of non-PT-symmetric harmonic-Gaussian potential. The interactions of
two bright solitons are also illustrated in PT-symmetric potentials. Finally,
we consider nonlinear modes and transverse power-flows in the three-dimensional
(3D) GP equation with the generalized PT-symmetric Scarf-II potential
