Inverse scattering solutions and dynamics for a nonlocal nonlinear Gross–Pitaevskii equation with PT-symmetric external potentials

Abstract A generalized nonlocal nonlinear Gross–Pitaevskii(GP) equation is presented, which can be reduced to the nonlocal GP equation with self-induced PT -symmetric potential. We derive some novel non-autonomous soliton solutions of nonlocal GP equation via inverse scattering and similarity transformations. These obtained solutions have singularities and are not the standard soliton solutions, here they can be called soliton-like(SL) solutions. Then we consider some controllable behaviors of these non-autonomous wave solutions. The obtained results are different from the solutions of the local nonlinear GP equation. Some propagation phenomena are produced through manipulating non-autonomous SL waves, which can present the potential applications to the soliton wave phenomena in nonlocal wave models.