报告题目：On the ground states and dynamics of space fractional nonlinear Schrodinger equation with rotational term and nonlocal nonlinear interactions.

报告人：张勇博士(Université de Rennes1，雷恩第一大学，法国)

时间：2015年12月25日13:30-14:30

地点：主楼1214

主持人：陈秀卿 教授

摘要：

In this work, we propose some efficient and robust numerical methods to compute 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 nonlocal interaction evaluation. To compute the ground states, we integrate the preconditioned Krylov subspace pseudospectral method  and the GauSum solver. For the dynamics simulation, using the rotating Lagrangian coordinates transform , we first reformulate the FSE into a new equation without rotation. Then, a time-splitting spectral scheme incorporated with the GauSum solver is proposed to simulate the new FSE. In parallel to the numerical schemes, we also prove some existence and nonexistence results for the ground states. Dynamical laws of some standard quantities, including the mass, energy, angular momentum and the center of mass, are stated. The ground states properties with respect to the fractional order and/or rotating frequencies, dynamics involving decoherence and turbulence together with some interesting phenomena are reported.