Probing non-locality of interactions in a Bose-Einstein condensate using solitons

We consider a Bose-Einstein condensate (BEC) with non-local inter-particle interactions. The local Gross-Pitaevskii (GP) equation is valid for the gas parameter nu =: a(3)n(0) << 1, but for nu -> 1, the BEC is described by a modified GP equation (MGPE). We study the exact solutions of the MGPE describing bright and dark solitons. It turns out that the width of these non-local solitons has qualitatively similar behaviour as the modified healing length due to the non-local interactions of the MGPE. We also study the effect of the non-locality and gas parameter (nu) on the stability of the solitons using the Vakhitov-Kolokolov (VK) stability criterion. We show that thew soliton solutions are stable according to the VK criterion. Further, the stability of these soliton solutions gets enhanced due to the non-locality of interactions.