Variational Approach to Study \mathcalPT-Symmetric Solitons in a Bose–Einstein Condensate with Non-locality of Interactions

Considering the non-locality of interactions in a Bose–Einstein condensate, the existence and stability of solitons subject to a \mathcalPT-symmetric potential are discussed. In the framework of the variational approach, we investigate how the non-locality of interactions affects the self-localization and stability of a condensate with attractive two-body interactions. The results reveal that the non-locality of interactions dramatically influences the shape, width, and chemical potential of the condensate. Analytically variational computation also predicts that there exists a critical negative non-local interaction strength (p_\rm c < 0) with each fixed two-body interaction (g_0 < 0), and there exists no bright soliton solution for p_0 < p_\rm c. Furthermore, we study the effect of the non-locality interactions on the stability of the solitons using the Vakhitov–Kolokolov stability criterion. It is shown that for a positive non-local interaction (p_0>0), there always exist stable bright solitons in some appropriate parameter regimes.