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We report the bright solitons of the generalized Gross-Pitaevskii (GP)equation with some types of physically relevant parity-time-(PT-) andnon-PT-symmetric potentials. We find that the constant momentum coefficient canmodulate the linear stability and complicated transverse power-flows (notalways from the gain toward loss) of nonlinear modes. However, the varyingmomentum coefficient Gamma(x) can modulate both unbroken linear PT-symmetricphases and stability of nonlinear modes. Particularly, the nonlinearity canexcite the unstable linear mode (i.e., broken linear PT-symmetric phase) tostable nonlinear modes. Moreover, we also find stable bright solitons in thepresence of non-PT-symmetric harmonic-Gaussian potential. The interactions oftwo 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

On stable solitons and interactions of the generalized Gross-Pitaevskii equation with PT-and non-PT-symmetric potentials