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

## TL;DR

This paper investigates stable bright solitons and their interactions in the generalized Gross-Pitaevskii equation with PT- and non-PT-symmetric potentials, revealing how momentum modulation affects stability and power flows.

## Contribution

It introduces new insights into the stability and dynamics of solitons under various PT-symmetric and non-PT-symmetric potentials, including the effects of momentum coefficients.

## Key findings

- Constant momentum modulates stability and power flows.
- Varying momentum coefficient influences PT-symmetry phases.
- Stable solitons exist in non-PT-symmetric harmonic-Gaussian potentials.

## Abstract

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