论文标题
非线性schrödinger方程的涡流存在
Existence of Vortices for Nonlinear Schrödinger Equations
论文作者
论文摘要
在本文中，我们研究了分别由Bose-Einstein冷凝物和几何学光学参数引起的两种非线性Schrödinger方程的涡旋存在。对于Bose-Einstein凝结参数的Gross-Pitaevskii方程，我们引入了相应功能是强制性的加权Sobolev空间。通过使用变分方法，我们证明在不同类型的边界条件下存在正和径向对称解。我们研究了通过约束最小化方法由几何光学论证引起的另一个方程式。此外，还得出了波传播常数的一些明确估计。
In this paper, we study the existence of vortices for two kinds of nonlinear Schrödinger equations arising from the Bose-Einstein condensates and geometric optics arguments, respectively. For the Gross-Pitaevskii equation from Bose-Einstein condensates arguments, we introduce the weighted Sobolev space on which the corresponding functional is coercive. By using the variational methods, we prove the existence of positive and radially symmetric solutions under different types of boundary condition. And we study another equation arising from geometric optics arguments by constrained minimization method. Furthermore some explicit estimates for the bound of the wave propagation constant are also derived.
