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

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 G 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 G(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 Scarff-II potential.