On the ground states and dynamics of space fractional nonlinear Schrödinger/Gross-Pitaevskii equations with rotation term and nonlocal nonlinear interactions

Abstract

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

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Cited by in corpus (6)

• Symmetry breaking of spatial Kerr solitons in fractional dimension
• Accurate and efficient computation of nonlocal potentials based on Gaussian-sum approximation
• Localized modes in nonlinear fractional systems with deep lattices
• A robust and efficient numerical method to compute the dynamics of the rotating two-component dipolar Bose-Einstein condensates
• A Jacobi spectral method for computing eigenvalue gaps and their distribution statistics of the fractional Schrödinger operator
• Normalized solutions for a coupled fractional schrodinger system in low dimensions