论文标题
计算旋转非线性Schrödinger方程的动作基态
Computing the action ground state for the rotating nonlinear Schrödinger equation
论文作者
论文摘要
我们考虑旋转非线性Schrödinger方程的动作基态的计算。它读起来是在Nehari约束下的作用功能的最小化。在聚焦案例中，我们确定了简化约束的问题的等效公式。基于它，我们提出了一种具有渐近拉格朗日乘数的归一化梯度流量方法，并建立了能源销售属性。流行优化方法也用于提高效率。在散落的情况下，我们证明可以通过无约束的最小化获得基态。然后应用直接梯度流量法和不受约束的优化方法。数值实验显示了两种情况下提出方法的收敛性和准确性，并讨论了效率的比较。最后，对动作与能量基态之间的关系进行了数值研究。
We consider the computations of the action ground state for a rotating nonlinear Schrödinger equation. It reads as a minimization of the action functional under the Nehari constraint. In the focusing case, we identify an equivalent formulation of the problem which simplifies the constraint. Based on it, we propose a normalized gradient flow method with asymptotic Lagrange multiplier and establish the energy-decaying property. Popular optimization methods are also applied to gain more efficiency. In the defocusing case, we prove that the ground state can be obtained by the unconstrained minimization. Then the direct gradient flow method and unconstrained optimization methods are applied. Numerical experiments show the convergence and accuracy of the proposed methods in both cases, and comparisons on the efficiency are discussed. Finally, the relation between the action and the energy ground states are numerically investigated.
