On 3d dipolar Bose-Einstein condensates involving quantum fluctuations and three-body interactions

Yongming Luo, Athanasios Stylianou

We study the following nonlocal mixed order Gross-Pitaevskii equation $$i{\partial }_t\psi =-\frac{1}{2}\Delta \psi +V_{ext}\psi +{\lambda }_1|\psi {|}^2\psi +{\lambda }_2(K\ast |\psi {|}^2)\psi +{\lambda }_3|\psi {|}^{p-2}\psi ,$$ where $K$ i…