Variational Approach to Study -Symmetric Solitons in a Bose–Einstein Condensate with Non-locality of Interactions**Supported by the National Natural Science Foundation of China under Grant Nos 11647017, 11805116 and 21703166, and the Science Research Fund of Shaanxi University of Science and Technology under Grant No BJ16-03.

Abstract

Considering the non-locality of interactions in a Bose–Einstein condensate, the existence and stability of solitons subject to a -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 (pc < 0) with each fixed two-body interaction (g0 < 0), and there exists no bright soliton solution for p0 < pc. 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 (p0 > 0), there always exist stable bright solitons in some appropriate parameter regimes.