On the ground states and dynamics of space fractional nonlinear Schrödinger/Gross-Pitaevskii equations with rotation term and nonlocal nonlinear interactions
arXiv:1512.03210 · doi:10.1016/j.jcp.2016.08.009
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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- 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