Non-autonomous rational soliton bound states and dynamics in the nonlocal Gross–Pitaevskii equation with a PT-symmetric potential

Abstract

This paper investigates an integrable Gross–Pitaevskii equation with nonlocal nonlinear effects, which consists of a nonlocal nonlinear Schrödinger equation adding an external potential function. The generalized Darboux transformation is used to solve this equation directly. We obtain rational solitons that exhibit the coexistence of dark and anti-dark solitons in bound states, and numerical simulations verify the correctness and robustness of these solutions. The influence of nonlocal effects and external potentials on the solutions of rational-type solitons is discussed. Results demonstrated that the dynamical behaviors of these solutions are novel and distinct from those of the local Gross–Pitaevskii equation and nonlocal nonlinear Schrödinger equation, providing some help and guidance for the realization of various soliton bound states in optical experiments.