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In this paper, we propose some efficient and robust numerical methods tocompute the ground states and dynamics of Fractional Schr\"{o}dinger Equation(FSE) with a rotation term and nonlocal nonlinear interactions. In particular,a newly developed Gaussian-sum (GauSum) solver is used for the nonlocalinteraction evaluation \cite{EMZ2015}. To compute the ground states, weintegrate the preconditioned Krylov subspace pseudo-spectral method \cite{AD1}and the GauSum solver. For the dynamics simulation, using the rotatingLagrangian coordinates transform \cite{BMTZ2013}, we first reformulate the FSEinto a new equation without rotation. Then, a time-splitting pseudo-spectralscheme incorporated with the GauSum solver is proposed to simulate the new FSE.

journal of computational physics

On the ground states and dynamics of space fractional nonlinear  Schr\"{o}dinger/Gross-Pitaevskii equations with rotation term and nonlocal  nonlinear interactions